Verfügbarkeit: Geometric properties of Banach spaces and nonlinear iterations

Geometric properties of Banach spaces and nonlinear iterations:

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Chidume, Charles (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	London Springer 2009
Schriftenreihe:	Lecture notes in mathematics 1965
Schlagworte:	Banach, Espaces de Banach spaces Banach-Raum Geometrie Iterationstheorie Nichtlineare Funktionalanalysis
Online-Zugang:	Cover Vorwort 1 Kapitel 1 Inhaltsverzeichnis
Beschreibung:	XVII, 326 S.
ISBN:	9781848821897

Internformat

MARC


LEADER	00000nam a2200000 cb4500
001	BV035440721
003	DE-604
005	20150512
007	t
008	090420s2009 \|\|\|\| 00\|\|\| eng d
020			\|a 9781848821897 \|9 978-1-84882-189-7
024	3		\|a 9781848821897
035			\|a (OCoLC)305125310
035			\|a (DE-599)DNB990359697
040			\|a DE-604 \|b ger
041	0		\|a eng
049			\|a DE-91G \|a DE-706 \|a DE-824 \|a DE-355 \|a DE-83 \|a DE-11 \|a DE-188 \|a DE-20
050		0	\|a QA3
082	0		\|a 515.732
084			\|a SI 850 \|0 (DE-625)143199: \|2 rvk
084			\|a SK 600 \|0 (DE-625)143248: \|2 rvk
084			\|a MAT 462f \|2 stub
084			\|a 47J25 \|2 msc
084			\|a 46B20 \|2 msc
084			\|a MAT 652f \|2 stub
084			\|a MAT 476f \|2 stub
100	1		\|a Chidume, Charles \|e Verfasser \|4 aut
245	1	0	\|a Geometric properties of Banach spaces and nonlinear iterations \|c Charles Chidume
264		1	\|a London \|b Springer \|c 2009
300			\|a XVII, 326 S.
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
490	1		\|a Lecture notes in mathematics \|v 1965
650		4	\|a Banach, Espaces de
650		4	\|a Banach spaces
650	0	7	\|a Banach-Raum \|0 (DE-588)4004402-6 \|2 gnd \|9 rswk-swf
650	0	7	\|a Geometrie \|0 (DE-588)4020236-7 \|2 gnd \|9 rswk-swf
650	0	7	\|a Iterationstheorie \|0 (DE-588)4027855-4 \|2 gnd \|9 rswk-swf
650	0	7	\|a Nichtlineare Funktionalanalysis \|0 (DE-588)4042093-0 \|2 gnd \|9 rswk-swf
689	0	0	\|a Banach-Raum \|0 (DE-588)4004402-6 \|D s
689	0	1	\|a Geometrie \|0 (DE-588)4020236-7 \|D s
689	0	2	\|a Nichtlineare Funktionalanalysis \|0 (DE-588)4042093-0 \|D s
689	0	3	\|a Iterationstheorie \|0 (DE-588)4027855-4 \|D s
689	0		\|C b \|5 DE-604
776	0	8	\|i Erscheint auch als \|n Online-Ausgabe \|z 978-1-84882-190-3
830		0	\|a Lecture notes in mathematics \|v 1965 \|w (DE-604)BV000676446 \|9 1965
856	4		\|m DE-576;springer \|q image/jpeg \|u http://swbplus.bsz-bw.de/bsz305210122cov.htm \|v 20090407020615 \|3 Cover
856	4		\|m DE-576;springer \|q application/pdf \|u http://swbplus.bsz-bw.de/bsz305210122vor.htm \|v 20090407021127 \|3 Vorwort 1
856	4		\|m DE-576;springer \|q application/pdf \|u http://swbplus.bsz-bw.de/bsz305210122kap.htm \|v 20090407021123 \|3 Kapitel 1
856	4	2	\|m DNB Datenaustausch \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017360986&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
999			\|a oai:aleph.bib-bvb.de:BVB01-017360986

Datensatz im Suchindex

_version_	1804138887229997056
adam_text	CONTENTS 1 SOME GEOMETRIC PROPERTIES OF BANACH SPACES . . . . . . . . . . . . 1 1.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 UNIFORMLY CONVEX SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 STRICTLY CONVEX BANACH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 THE MODULUS OF CONVEXITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 UNIFORM CONVEXITY, STRICT CONVEXITY AND REFLEXIVITY . . . . . . . . 7 1.6 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 SMOOTH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 THE MODULUS OF SMOOTHNESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 DUALITY BETWEEN SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 DUALITY MAPS IN BANACH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.1 MOTIVATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 DUALITY MAPS OF SOME CONCRETE SPACES. . . . . . . . . . . . . . . . . . . . 23 3.3 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4 INEQUALITIES IN UNIFORMLY CONVEX SPACES . . . . . . . . . . . . . . . . . . 29 4.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2 BASIC NOTIONS OF CONVEX ANALYSIS. . . . . . . . . . . . . . . . . . . . . . . . . 30 4.3 P -UNIFORMLY CONVEX SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.4 UNIFORMLY CONVEX SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.5 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5 INEQUALITIES IN UNIFORMLY SMOOTH SPACES . . . . . . . . . . . . . . . . . 45 5.1 DEFINITIONS AND BASIC THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.2 Q * UNIFORMLY SMOOTH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.3 UNIFORMLY SMOOTH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 XIII XIV CONTENTS 5.4 CHARACTERIZATION OF SOME REAL BANACH SPACES BY THE DUALITY MAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.4.1 DUALITY MAPS ON UNIFORMLY SMOOTH SPACES . . . . . . . . . . 51 5.4.2 DUALITY MAPS ON SPACES WITH UNIFORMLY G* ATEAUX DIFFERENTIABLE NORMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6 ITERATIVE METHOD FOR FIXED POINTS OF NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.2 ASYMPTOTIC REGULARITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.3 UNIFORM ASYMPTOTIC REGULARITY . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.4 STRONG CONVERGENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 6.5 WEAK CONVERGENCE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6.6 SOME EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.7 HALPERN-TYPE ITERATION METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.7.1 CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.7.2 THE CASE OF NON-SELF MAPPINGS . . . . . . . . . . . . . . . . . . . . 80 6.8 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 7 HYBRID STEEPEST DESCENT METHOD FOR VARIATIONAL INEQUALITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.2 PRELIMINARIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 7.3 CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 7.4 FURTHER CONVERGENCE THEOREMS. . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7.4.1 CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7.5 THE CASE OF L P SPACES, 1 * 2 . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.6 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 8 ITERATIVE METHODS FOR ZEROS OF * * ACCRETIVE-TYPE OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 8.1 INTRODUCTION AND PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 8.2 SOME REMARKS ON ACCRETIVE OPERATORS . . . . . . . . . . . . . . . . . . . . 116 8.3 LIPSCHITZ STRONGLY ACCRETIVE MAPS . . . . . . . . . . . . . . . . . . . . . . . . 117 8.4 GENERALIZED PHI-ACCRETIVE SELF-MAPS . . . . . . . . . . . . . . . . . . . . . . 120 8.5 GENERALIZED PHI-ACCRETIVE NON-SELF MAPS . . . . . . . . . . . . . . . . . . 124 8.6 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 9 ITERATION PROCESSES FOR ZEROS OF GENERALIZED * * ACCRETIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 9.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 9.2 UNIFORMLY CONTINUOUS GENERALIZED * -HEMI-CONTRACTIVE MAPS . 130 9.3 GENERALIZED LIPSCHITZ, GENERALIZED * -QUASI-ACCRETIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 9.4 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 CONTENTS XV 10 AN EXAMPLE; MANN ITERATION FOR STRICTLY PSEUDO-CONTRACTIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 10.1 INTRODUCTION AND A CONVERGENCE THEOREM . . . . . . . . . . . . . . . . . 141 10.2 AN EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 10.3 MANN ITERATION FOR A CLASS OF LIPSCHITZ PSEUDO-CONTRACTIVE MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 10.4 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 11 APPROXIMATION OF FIXED POINTS OF LIPSCHITZ PSEUDO-CONTRACTIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 11.1 ITERATION METHODS FOR LIPSCHITZ PSEUDO-CONTRACTIONS . . . . . . . . 151 11.2 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 12 GENERALIZED LIPSCHITZ ACCRETIVE AND PSEUDO-CONTRACTIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 12.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 12.2 CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 12.3 SOME APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 12.4 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 13 APPLICATIONS TO HAMMERSTEIN INTEGRAL EQUATIONS . . . . . . . . . 169 13.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 13.2 SOLUTION OF HAMMERSTEIN EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . 169 13.2.1 CONVERGENCE THEOREMS FOR LIPSCHITZ MAPS . . . . . . . . . . 175 13.2.2 CONVERGENCE THEOREMS FOR BOUNDED MAPS . . . . . . . . . . . 177 13.2.3 EXPLICIT ALGORITHMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 13.3 CONVERGENCE THEOREMS WITH EXPLICIT ALGORITHMS . . . . . . . . . . . 179 13.3.1 SOME USEFUL LEMMAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 13.3.2 CONVERGENCE THEOREMS WITH COUPLED SCHEMES FOR THE CASE OF LIPSCHITZ MAPS . . . . . . . . . . . . . . . . . . . . . 180 13.3.3 CONVERGENCE IN L P , 1 * 2 . . . . . . . . . . . . . . . . . . . . . . 183 13.4 COUPLED SCHEME FOR THE CASE OF BOUNDED OPERATORS . . . . . . . . 185 13.4.1 CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 13.4.2 CONVERGENCE FOR BOUNDED OPERATORS IN L P SPACES, 1 * 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 13.4.3 CONVERGENCE THEOREMS FOR GENERALIZED LIPSCHITZ MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 13.5 REMARKS AND OPEN QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 13.6 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 14 ITERATIVE METHODS FOR SOME GENERALIZATIONS OF NONEXPANSIVE MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 14.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 14.2 ITERATION METHODS FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 14.2.1 MODIFIED MANN PROCESS . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 XVI CONTENTS 14.2.2 ITERATION METHOD OF SCHU . . . . . . . . . . . . . . . . . . . . . . . . . . 197 14.2.3 HALPERN-TYPE PROCESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 14.3 ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS. . . . . . . . . . . . . . 200 14.4 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 15 COMMON FIXED POINTS FOR FINITE FAMILIES OF NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 15.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 15.2 CONVERGENCE THEOREMS FOR A FAMILY OF NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 15.3 NON-SELF MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 16 COMMON FIXED POINTS FOR COUNTABLE FAMILIES OF NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 16.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 16.2 PATH CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 16.3 PATH CONVERGENCE IN UNIFORMLY CONVEX REAL BANACH SPACES . 220 16.4 ITERATIVE CONVERGENCE IN UNIFORMLY CONVEX REAL BANACH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 16.5 NON-SELF MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 16.6 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 17 COMMON FIXED POINTS FOR FAMILIES OF COMMUTING NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 17.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 17.2 THREE COMMUTING NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . 232 17.3 COMMON FIXED POINTS FOR FAMILY OF COMMUTING NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 17.4 CONVERGENCE THEOREMS FOR INFINITE FAMILY OF COMMUTING NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 17.5 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 18 FINITE FAMILIES OF LIPSCHITZ PSEUDO-CONTRACTIVE AND ACCRETIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 18.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 18.2 CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 18.3 FINITE FAMILIES OF LIPSCHITZ ACCRETIVE OPERATORS . . . . . . . . . . . . 249 18.4 SOME APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 18.5 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 19 GENERALIZED LIPSCHITZ PSEUDO-CONTRACTIVE AND ACCRETIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 19.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 19.2 GENERALIZED LIPSCHITZ PSEUDO-CONTRACTIVE MAPPINGS . . . . . . . . . 251 19.3 GENERALIZED LIPSCHITZ ACCRETIVE OPERATORS . . . . . . . . . . . . . . . . . 255 19.4 SOME APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 19.5 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 CONTENTS XVII 20 FINITE FAMILIES OF NON-SELF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 20.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 20.2 PRELIMINARIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 20.3 STRONG CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 20.4 WEAK CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 20.5 THE CASE FOR NONEXPANSIVE MAPPINGS . . . . . . . . . . . . . . . . . . . . . 269 20.6 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 21 FAMILIES OF TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPS . . . . . 271 21.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 21.2 CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 21.2.1 NECESSARY AND SUFFICIENT CONDITIONS FOR CONVERGENCE IN REAL BANACH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 21.2.2 CONVERGENCE THEOREM IN REAL UNIFORMLY CONVEX BANACH SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 21.3 THE CASE OF NON-SELF MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 21.4 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 22 COMMON FIXED POINTS FOR ONE-PARAMETER NONEXPANSIVE SEMIGROUP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 22.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 22.2 EXISTENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 22.3 CONVERGENCE THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 22.4 HISTORICAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 23 SINGLE-VALUED ACCRETIVE OPERATORS; APPLICATIONS; SOME OPEN QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 23.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 23.2 LOWER SEMI-CONTINUOUS ACCRETIVE OPERATORS ARE SINGLE-VALUED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 23.3 AN APPLICATION TO VARIATIONAL INEQUALITIES . . . . . . . . . . . . . . . . . 293 23.4 GENERAL COMMENTS ON SOME FIXED POINT THEOREMS . . . . . . . . . 295 23.5 EXAMPLES OF ACCRETIVE OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . 296 23.6 EXAMPLES OF NONEXPANSIVE RETRACTS. . . . . . . . . . . . . . . . . . . . . . . 297 23.7 SOME QUESTIONS OF INTEREST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 23.8 FURTHER READING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
any_adam_object	1
author	Chidume, Charles
author_facet	Chidume, Charles
author_role	aut
author_sort	Chidume, Charles
author_variant	c c cc
building	Verbundindex
bvnumber	BV035440721
callnumber-first	Q - Science
callnumber-label	QA3
callnumber-raw	QA3
callnumber-search	QA3
callnumber-sort	QA 13
callnumber-subject	QA - Mathematics
classification_rvk	SI 850 SK 600
classification_tum	MAT 462f MAT 652f MAT 476f
ctrlnum	(OCoLC)305125310 (DE-599)DNB990359697
dewey-full	515.732
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
dewey-raw	515.732
dewey-search	515.732
dewey-sort	3515.732
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02464nam a2200589 cb4500</leader><controlfield tag="001">BV035440721</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150512 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">090420s2009 \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781848821897</subfield><subfield code="9">978-1-84882-189-7</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9781848821897</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)305125310</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB990359697</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA3</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.732</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 462f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">47J25</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">46B20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 652f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 476f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chidume, Charles</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometric properties of Banach spaces and nonlinear iterations</subfield><subfield code="c">Charles Chidume</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London</subfield><subfield code="b">Springer</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVII, 326 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">1965</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Banach, Espaces de</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Banach spaces</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Banach-Raum</subfield><subfield code="0">(DE-588)4004402-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrie</subfield><subfield code="0">(DE-588)4020236-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Iterationstheorie</subfield><subfield code="0">(DE-588)4027855-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Funktionalanalysis</subfield><subfield code="0">(DE-588)4042093-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Banach-Raum</subfield><subfield code="0">(DE-588)4004402-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Geometrie</subfield><subfield code="0">(DE-588)4020236-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Nichtlineare Funktionalanalysis</subfield><subfield code="0">(DE-588)4042093-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Iterationstheorie</subfield><subfield code="0">(DE-588)4027855-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="C">b</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-84882-190-3</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">1965</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">1965</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="m">DE-576;springer</subfield><subfield code="q">image/jpeg</subfield><subfield code="u">http://swbplus.bsz-bw.de/bsz305210122cov.htm</subfield><subfield code="v">20090407020615</subfield><subfield code="3">Cover</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="m">DE-576;springer</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://swbplus.bsz-bw.de/bsz305210122vor.htm</subfield><subfield code="v">20090407021127</subfield><subfield code="3">Vorwort 1</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="m">DE-576;springer</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://swbplus.bsz-bw.de/bsz305210122kap.htm</subfield><subfield code="v">20090407021123</subfield><subfield code="3">Kapitel 1</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017360986&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-017360986</subfield></datafield></record></collection>
id	DE-604.BV035440721
illustrated	Not Illustrated
indexdate	2024-07-09T21:35:19Z
institution	BVB
isbn	9781848821897
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-017360986
oclc_num	305125310
open_access_boolean
owner	DE-91G DE-BY-TUM DE-706 DE-824 DE-355 DE-BY-UBR DE-83 DE-11 DE-188 DE-20
owner_facet	DE-91G DE-BY-TUM DE-706 DE-824 DE-355 DE-BY-UBR DE-83 DE-11 DE-188 DE-20
physical	XVII, 326 S.
publishDate	2009
publishDateSearch	2009
publishDateSort	2009
publisher	Springer
record_format	marc
series	Lecture notes in mathematics
series2	Lecture notes in mathematics
spelling	Chidume, Charles Verfasser aut Geometric properties of Banach spaces and nonlinear iterations Charles Chidume London Springer 2009 XVII, 326 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1965 Banach, Espaces de Banach spaces Banach-Raum (DE-588)4004402-6 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Iterationstheorie (DE-588)4027855-4 gnd rswk-swf Nichtlineare Funktionalanalysis (DE-588)4042093-0 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Geometrie (DE-588)4020236-7 s Nichtlineare Funktionalanalysis (DE-588)4042093-0 s Iterationstheorie (DE-588)4027855-4 s b DE-604 Erscheint auch als Online-Ausgabe 978-1-84882-190-3 Lecture notes in mathematics 1965 (DE-604)BV000676446 1965 DE-576;springer image/jpeg http://swbplus.bsz-bw.de/bsz305210122cov.htm 20090407020615 Cover DE-576;springer application/pdf http://swbplus.bsz-bw.de/bsz305210122vor.htm 20090407021127 Vorwort 1 DE-576;springer application/pdf http://swbplus.bsz-bw.de/bsz305210122kap.htm 20090407021123 Kapitel 1 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017360986&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Chidume, Charles Geometric properties of Banach spaces and nonlinear iterations Lecture notes in mathematics Banach, Espaces de Banach spaces Banach-Raum (DE-588)4004402-6 gnd Geometrie (DE-588)4020236-7 gnd Iterationstheorie (DE-588)4027855-4 gnd Nichtlineare Funktionalanalysis (DE-588)4042093-0 gnd
subject_GND	(DE-588)4004402-6 (DE-588)4020236-7 (DE-588)4027855-4 (DE-588)4042093-0
title	Geometric properties of Banach spaces and nonlinear iterations
title_auth	Geometric properties of Banach spaces and nonlinear iterations
title_exact_search	Geometric properties of Banach spaces and nonlinear iterations
title_full	Geometric properties of Banach spaces and nonlinear iterations Charles Chidume
title_fullStr	Geometric properties of Banach spaces and nonlinear iterations Charles Chidume
title_full_unstemmed	Geometric properties of Banach spaces and nonlinear iterations Charles Chidume
title_short	Geometric properties of Banach spaces and nonlinear iterations
title_sort	geometric properties of banach spaces and nonlinear iterations
topic	Banach, Espaces de Banach spaces Banach-Raum (DE-588)4004402-6 gnd Geometrie (DE-588)4020236-7 gnd Iterationstheorie (DE-588)4027855-4 gnd Nichtlineare Funktionalanalysis (DE-588)4042093-0 gnd
topic_facet	Banach, Espaces de Banach spaces Banach-Raum Geometrie Iterationstheorie Nichtlineare Funktionalanalysis
url	http://swbplus.bsz-bw.de/bsz305210122cov.htm http://swbplus.bsz-bw.de/bsz305210122vor.htm http://swbplus.bsz-bw.de/bsz305210122kap.htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017360986&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000676446
work_keys_str_mv	AT chidumecharles geometricpropertiesofbanachspacesandnonlineariterations

Verfügbarkeit

Es ist kein Print-Exemplar vorhanden.

Fernleihe Bestellen Achtung: Nicht im THWS-Bestand! Inhaltsverzeichnis

MARC

Datensatz im Suchindex

Es ist kein Print-Exemplar vorhanden.

Ähnliche Einträge