Sequence spaces and measures of noncompactness with applications to differential and integral equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Delhi [u.a.]
Springer
2014
|
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XII, 315 S. |
| ISBN: | 9788132218852 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042084680 | ||
| 003 | DE-604 | ||
| 005 | 20141022 | ||
| 007 | t | ||
| 008 | 140922s2014 |||| 00||| eng d | ||
| 020 | |a 9788132218852 |9 978-81-322-1885-2 | ||
| 024 | 3 | |a 9788132218869 | |
| 035 | |a (OCoLC)895466281 | ||
| 035 | |a (DE-599)BVBBV042084680 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Banaś, Józef |d 1950- |e Verfasser |0 (DE-588)1046152416 |4 aut | |
| 245 | 1 | 0 | |a Sequence spaces and measures of noncompactness with applications to differential and integral equations |c Józef Banaś ; Mohammad Mursaleen |
| 264 | 1 | |a New Delhi [u.a.] |b Springer |c 2014 | |
| 300 | |a XII, 315 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Mursaleen, Mohammad |d 1953- |e Verfasser |0 (DE-588)1059145480 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-81-322-1886-9 |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027525685&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027525685&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027525685 | ||
Datensatz im Suchindex
| _version_ | 1804152537996066816 |
|---|---|
| adam_text | Contents
Introduction to FK Spaces
.............................. 1
1.1
Classical Sequence Spaces
...........................
I
1.2
Linear Metric Spaces
............................... 3
1.3
Paranormed Spaces
................................ 5
1
A FK and BK Spaces.
................................ 10
1.5
Matrix Domains
.................................. 18
1.6
Sequence Spaces of Matrix Domains
.................... 23
References
.......................................... 30
Matrix Transformations
................................ 33
2.1
Continuous Duals
................................. 33
2.2 Köthe-Toeplitz
Duals
.............................. 39
2.3
Other Duals
..................................... 47
2.4
Multiplier Spaces
.................................. 48
2.5
Matrix Classes of Some FK and BK Spaces
............... 52
2.6
Conservative, Regular, and
Schur
Matrices
................ 57
2.7
Matrix Transformations for Matrix Domains
............... 64
References
.......................................... 70
Some New Sequence Spaces of Non-absolute Type
............ 71
3.1
λ—
sequence Spaces
................................ 71
3.2
Some Inclusion Relations
............................ 76
3.3
Duals of the Spaces of
λ
-sequences
....................
85
3.4
Certain Matrix Mappings on
λ—
sequence Spaces
..........., 93
References
.......................................... 102
Some Non-classical Sequence Spaces
....................... 105
4.1
Sequence Spaces of Maddox
.......................... 105
4:2
Echelon and Coechelon Spaces
........................
Ill
4.3
Matrix Transformations of Maddox Sequence Spaces
........ 114
4.4
Applications
.....................-............... 119
4.5
Matrix Transformations Between the Spaces A l X
.......... 130
vu
viii Contents
4.6
Sequence Spaces of Sargent
.......................... 133
4.7
Matrix Transformations on and into
т(ф)
and
η {φ)..........
137
References
.......................................... 145
5
Measures of Non-compactness
........................... 147
5.1
Preliminaries
..................................... 147
5.2
The Kuratowski Measure of Non-compactness
............. 150
5.3
The Hausdorff Measure of Non-compactness
.............. 154
5.4
The Hausdorff Measure of Non-compactness
for Some Sequence Spaces
........................... 161
5.5
The Hausdorff Measure of Non-compactness
for Some Function Spaces
........................... 163
5.6
Inner Hausdorff Measure of Non-compactness
............. 166
5.7
The
Istrăţescu
Measure of Non-compactness
............... 168
5.8
Axiomatic Approach to the Concept of a Measure
of Non-compactness
................................ 168
5.9
Measure of Non-compactness of Operators
and Condensing Operators
........................... 175
References
.......................................... 183
6
Application to Compact Matrix Operators
.................. 185
6.1
Compact Matrix Operators on Some Classical
Sequence Spaces
.................................. 186
6.2
Compact Matrix Operators on Some BK Spaces
............ 189
6.3
Applications to Some Matrix Domains
................... 199
6.4
Compact Operators Between the Spaces Related to £p
........ 209
References
.......................................... 217
7
Applications to Infinite Systems of Differential Equations
....... 219
7.1
Ordinary Differential Equations in Banach Spaces
........... 220
7.2
Some Special Results Concerning Differential
Equations in Banach Spaces
.......................... 228
7.3
Infinite Systems of Differential Equations in the Space cq
..... 230
7.4
Infinite Systems of Differential Equations in the Space
с
...... 234
7.5
The Case of the Sequence Spaces f and tp
............... 241
7.6
Infinite Systems of Differential Equations in the Space £x
..... 246
References
.......................................... 261
8
Applications to Integral Equations
........................ 263
8.1
The Existence and Attractivity of Solutions of a Quadratic
Volteira
integral Equation
........................... 264
8.2
An Infinite System of Integral Equations of Volterra
Type in the Space
сц
............................... 274
Contents ix
8.3
Solvability of a Class of Nonlinear Integral
Equations of Volterra-Stieltjes Type
.................... 281
8.4
Solvability of an Infinite System of Nonlinear
Volterra-Stieltjes Integral Equations
.................... 296
References
.......................................... 309
Appendix
............................................. 311
Index
................................................ 313
Józef Banaś
· Mohammad Mursaleen
Sequence Spaces and Measures of Noncompactness with
Applications to Differential and Integral Equations
This book deals with the study of sequence spaces, matrix transformations, measures
of noncompactness and their various applications. The notion of measure of
noncompactness is one of the most useful ones available and has many applications.
The book discusses some of the existence results for various types of differential and
integral equations with the help of measures of noncompactness; in particular, the
Hausdorff measure of noncompactness has been applied to obtain necessary and
sufficient conditions for matrix operators between BK spaces to be compact operators.
The book consists of eight self-contained chapters. Chapter
ι
discusses the theory of FK
spaces and Chapter
2
various duals of sequence spaces, which are used to characterize
the matrix classes between these sequence spaces (FK and BK spaces) in Chapters
3
and
4.
Chapter
5
studies the notion of a measure of noncompactness and its properties.
The techniques associated with measures of noncompactness are applied to characterize
the compact matrix operators in Chapters
6.
In Chapters
7
and
8,
some of the existence
results are discussed for various types of differential and integral equations, which are
obtained with the help of argumentations based on compactness conditions.
|
| any_adam_object | 1 |
| author | Banaś, Józef 1950- Mursaleen, Mohammad 1953- |
| author_GND | (DE-588)1046152416 (DE-588)1059145480 |
| author_facet | Banaś, Józef 1950- Mursaleen, Mohammad 1953- |
| author_role | aut aut |
| author_sort | Banaś, Józef 1950- |
| author_variant | j b jb m m mm |
| building | Verbundindex |
| bvnumber | BV042084680 |
| ctrlnum | (OCoLC)895466281 (DE-599)BVBBV042084680 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042084680 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:12:18Z |
| institution | BVB |
| isbn | 9788132218852 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027525685 |
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| physical | XII, 315 S. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
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| publisher | Springer |
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| spelling | Banaś, Józef 1950- Verfasser (DE-588)1046152416 aut Sequence spaces and measures of noncompactness with applications to differential and integral equations Józef Banaś ; Mohammad Mursaleen New Delhi [u.a.] Springer 2014 XII, 315 S. txt rdacontent n rdamedia nc rdacarrier Mursaleen, Mohammad 1953- Verfasser (DE-588)1059145480 aut Erscheint auch als Online-Ausgabe 978-81-322-1886-9 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027525685&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027525685&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Banaś, Józef 1950- Mursaleen, Mohammad 1953- Sequence spaces and measures of noncompactness with applications to differential and integral equations |
| title | Sequence spaces and measures of noncompactness with applications to differential and integral equations |
| title_auth | Sequence spaces and measures of noncompactness with applications to differential and integral equations |
| title_exact_search | Sequence spaces and measures of noncompactness with applications to differential and integral equations |
| title_full | Sequence spaces and measures of noncompactness with applications to differential and integral equations Józef Banaś ; Mohammad Mursaleen |
| title_fullStr | Sequence spaces and measures of noncompactness with applications to differential and integral equations Józef Banaś ; Mohammad Mursaleen |
| title_full_unstemmed | Sequence spaces and measures of noncompactness with applications to differential and integral equations Józef Banaś ; Mohammad Mursaleen |
| title_short | Sequence spaces and measures of noncompactness with applications to differential and integral equations |
| title_sort | sequence spaces and measures of noncompactness with applications to differential and integral equations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027525685&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027525685&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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