Differential subordinations: theory and applications
"Examining a topic that has been the subject of more than 300 articles since it was first conceived nearly 20 years ago, this monograph describes for the first time in one volume the basic theory and multitude of applications in the study of differential subordinations."--BOOK JACKET.
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Marcel Dekker
2000
|
| Schriftenreihe: | Pure and Applied Mathematics
225 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Examining a topic that has been the subject of more than 300 articles since it was first conceived nearly 20 years ago, this monograph describes for the first time in one volume the basic theory and multitude of applications in the study of differential subordinations."--BOOK JACKET. |
| Beschreibung: | XI, 459 Seiten graph. Darst. |
| ISBN: | 0824700295 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Differential subordinations
Autor: Miller, Sanford S
Jahr: 2000
CONTENTS
Preface v
Chapter 1
Preliminaries
1.1. A Short History................................................ 1
1.2. Basic Definitions and Results....................................3
a. Subordination ..............................................4
b. Hypergeometric Functions ...................................5
c. Classes of Functions.........................................7
d. Integral Operators.......................................... 10
Chapter 2
Theory of Second-Order Differential Subordinations
2.1. Introduction ................................................ 13
2.2. Fundamental Lemmas........................................ 18
2.3. Admissible Functions and Fundamental Theorems............... 27
2.4. Examples.................................................. 36
2.5. The Open Door Lemma and the Integral Existence Theorem...... 44
2.6. Classical Results of Geometric Function Theory Revisited........ 56
ix
X
CONTENTS
Chapter 3
Applications of First-Order Differential Subordinations
3.1. First-Order Linear Differential Subordinations....................................69
3,2 Briot-Bouquet Differential Subordinations..........................................80
3.3. Briot-Bouquet Applications in Univalent Function Theory ...... 103
3.4 Generalized Briot-Bouquet Differential Subordinations..................120
3.5. Analytic Integral Operators Between Classes of Functions............145
3.6. Subordination-Preserving Integral Operators .................................174
Chapter 4
Applications of Second-Order Differential Subordinations
4.1. Second-Order Linear Differential Subordinations ............................187
4.2 Integral Operators Preserving Functions With Positive Real Part . 201
4.3. Integral Operators Preserving Bounded Functions ..........................207
4.4. Averaging Integral Operators ..............................................................214
4.5. Hypergeometric Functions....................................................................230
4.6. The Schwarzian and Starlikeness ........................................................244
Chapter 5
Special Differential Subordinations
5.1. Conditions for Special Subclasses of Starlike Functions..................249
5.2. Simple Conditions for Starlikeness and Convexity ..........................269
5.3. On a Theorem of Robertson..................................................................284
5.4. Subordination by Convex Functions..................................................289
5.5. Functions with Bounded Turning and Starlike Functions ..............292
5.6. Functions Starlike with Respect to Symmetric Points......................313
CONTENTS xi
Chapter 6
Higher Order Differential Subordinations
6.1. Introduction.............................................. 319
6.2. Third-Order Differential Subordinations....................... 322
6.3 The Euler Nth-Order Differential Subordination................ 334
Chapter 7
Differential Subordinations of Several Complex Variables
7.1 Preliminary Lemmas....................................... 341
7.2 Extensions of the Fundamental Lemma....................... 347
7.3 Dominants and Admissible Functions in C ................... 368
7.4 Differential Subordinations in c ........................... 373
Chapter 8
Applications of Differential Subordinations in Other Fields
8.1. Harmonic Functions ..............................................................................379
8.2. Meromorphic Functions........................................................................382
8.3. Differential Subordinations in the Upper Half-Plane ......................397
8.4 Extensions to Banach Spaces..............................................................408
Appendix Convexity of Bernoulli Functions ............................................415
Bibliography....................................................................................................421
List of Symbols ..............................................................................................449
Index ..................................................................................................................455
|
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| institution | BVB |
| isbn | 0824700295 |
| language | English |
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| spelling | Miller, Sanford S. Verfasser aut Differential subordinations theory and applications Sanford S. Miller, State University of New York, College at Brockport, Brockport, New York, Petru T. Mocanu, Babeş-Bolyai University, Cluj-Napoca, Romania New York, NY [u.a.] Marcel Dekker 2000 XI, 459 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and Applied Mathematics 225 "Examining a topic that has been the subject of more than 300 articles since it was first conceived nearly 20 years ago, this monograph describes for the first time in one volume the basic theory and multitude of applications in the study of differential subordinations."--BOOK JACKET. Inégalités différentielles ram Differential inequalities Functions of complex variables Differentialungleichung (DE-588)4149785-5 gnd rswk-swf Komplexe Differentialgleichung (DE-588)4161117-2 gnd rswk-swf Differentialungleichung (DE-588)4149785-5 s Komplexe Differentialgleichung (DE-588)4161117-2 s DE-604 Mocanu, Petru T. Verfasser aut Pure and Applied Mathematics 225 (DE-604)BV000001885 225 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009156349&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Miller, Sanford S. Mocanu, Petru T. Differential subordinations theory and applications Pure and Applied Mathematics Inégalités différentielles ram Differential inequalities Functions of complex variables Differentialungleichung (DE-588)4149785-5 gnd Komplexe Differentialgleichung (DE-588)4161117-2 gnd |
| subject_GND | (DE-588)4149785-5 (DE-588)4161117-2 |
| title | Differential subordinations theory and applications |
| title_auth | Differential subordinations theory and applications |
| title_exact_search | Differential subordinations theory and applications |
| title_full | Differential subordinations theory and applications Sanford S. Miller, State University of New York, College at Brockport, Brockport, New York, Petru T. Mocanu, Babeş-Bolyai University, Cluj-Napoca, Romania |
| title_fullStr | Differential subordinations theory and applications Sanford S. Miller, State University of New York, College at Brockport, Brockport, New York, Petru T. Mocanu, Babeş-Bolyai University, Cluj-Napoca, Romania |
| title_full_unstemmed | Differential subordinations theory and applications Sanford S. Miller, State University of New York, College at Brockport, Brockport, New York, Petru T. Mocanu, Babeş-Bolyai University, Cluj-Napoca, Romania |
| title_short | Differential subordinations |
| title_sort | differential subordinations theory and applications |
| title_sub | theory and applications |
| topic | Inégalités différentielles ram Differential inequalities Functions of complex variables Differentialungleichung (DE-588)4149785-5 gnd Komplexe Differentialgleichung (DE-588)4161117-2 gnd |
| topic_facet | Inégalités différentielles Differential inequalities Functions of complex variables Differentialungleichung Komplexe Differentialgleichung |
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