Differential Subordinations : Theory and Applications /: Theory and Applications. (2000)

• Record Type: Book
• Further Information: Note: Sanford S. Miller, Petru T. Mocanu.
• Authors: Miller, Sanford S; Mocanu, Petru T
• 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
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2000
• Extent: 1 online resource
• Subjects: 515/.36; Numerical analysis; Numerical analysis; Electronic books
• Languages: English
• ISBNs: 9781482289817; 1482289814
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.