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Differential Subordinations : Theory and Applications

Author: Sanford S Miller; Petru T Mocanu
Publisher: Boca Raton, FL : CRC Press, 2000.
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Edition/Format:   eBook : Document : English : First edition
Summary:
""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.""--Provided by publisher.
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sanford S Miller; Petru T Mocanu
ISBN: 9781482289817 1482289814
OCLC Number: 1027770324
Description: 1 online resource : text file, PDF
Contents: Cover; Half Title; Pure And Applied Mathematics; Monographs And Textbooks Inpure And Applied Mathematics; Title; Copyright; Thanks; Preface; Contents; Preface Chapter; Chapter 1 Preliminaries; 1.1. A Short History; 1.2. Basic Definitions And Results; A. Subordination; B. Hypergeometric Functions; C. Classes Of Functions; D. Integral Operators; Chapter 2 Theory Of Second-order Differential Subordinations; 2.1. Introduction; 2.2. Fundamental Lemmas; 2.3. Admissible Functions And Fundamental Theorems; 2.4. Examples; 2.5. The Open Door Lemma And The Integral Existence Theorem 2.6. Classical Results Of Geometric Function Theory RevisitedChapter 3 Applications Of First-order Differential Subordinations; 3.1. First-order Linear Differential Subordinations; 3.2 Briot-bouquet Differential Subordinations; 3.3. Briot-bouquet Applications In Univalent Function Theory; 3.4 Generalized Briot-bouquet Differential Subordinations; 3.5. Analytic Integral Operators Between Classes Of Functions; 3.6. Subordination- Preserving Integral Operators; Chapter 4 Applications Of Second-order Differential Subordinations; 4.1. Second-order Linear Differential Subordinations 4.2 Integral Operators Preserving Functions With Positive Real Part4.3. Integral Operators Preserving Bounded Functions; 4.4. Averaging Integral Operators; 4.5. Hypergeometric Functions; 4.6. The Schwarzian And Starlikeness; Chapter 5 Special Differential Subordinations; 5.1. Conditions For Special Subclasses Of Starlike Functions; 5.2. Simple Conditions For Starlikeness And Convexity; 5.3. On A Theorem Of Robertson; 5.4. Subordination By Convex Functions; 5.5. Functions With Bounded Turning And Starlike Functions; 5.6. Functions Starlike With Respect To Symmetric Points Chapter 6 Higher Order Differential Subordinations6.1. Introduction; 6.2. Third-order Differential Subordinations; 6.3 The Euler Nth-order Differential Subordination; Chapter 7 Differential Subordinations Of Several Complex Variables; 7.1. Preliminary Lemmas; 7.2 Extensions Of The Fundamental Lemma ... ... ... ... . 34; 7.3 Dominants And Admissible Functions In En; 7.4 Differential Subordinations In En; 8.2. Meromorphic Functions; Chapter 8 Applications Of Differentialsubordinations In Other Fields; 8.1. Harmonic Functions; 8.2. Meromorphic Functions 8.3. Differential Subordinations In The Upper Half- Plane8.4 Extensions To Banach Spaces; Appendix Convexity Of Bernoulli Functions; Bibliography; List Of Symbols; Untitled; Index
Series Title: Chapman & Hall/CRC Pure and Applied Mathematics
Responsibility: Sanford S. Miller, Petru T. Mocanu.

Abstract:

""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.""--Provided by publisher.

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