| Preface |
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1 | (2) |
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Basic Definitions and Results |
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3 | (10) |
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4 | (1) |
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5 | (2) |
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7 | (3) |
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10 | (3) |
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Theory of Second-Order Differential Subordinations |
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13 | (5) |
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18 | (9) |
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Admissible Functions and Fundamental Theorems |
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27 | (9) |
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36 | (8) |
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The Open Door Lemma and the Integral Existence Theorem |
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44 | (12) |
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Classical Results of Geometric Function Theory Revisited |
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56 | (13) |
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Applications of First-Order Differential Subordinations |
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First- Order Linear Differential Subordinations |
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69 | (11) |
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Briot-Bouquet Differential Subordinations |
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80 | (23) |
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Briot-Bouquet Applications in Univalent Function Theory |
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103 | (17) |
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Generalized Briot-Bouquet Differential Subordinations |
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120 | (25) |
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Analytic Integral Operators Between Classes of Functions |
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145 | (29) |
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Subordination-Preserving Integral Operators |
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174 | (13) |
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Applications of Second-Order Differential Subordinations |
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Second-Order Linear Differential Subordinations |
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187 | (14) |
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Integral Operators Preserving Functions With Positive Real Part |
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201 | (6) |
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Integral Operators Preserving Bounded Functions |
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207 | (7) |
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Averaging Integral Operators |
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214 | (16) |
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230 | (14) |
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The Schwarzian and Starlikeness |
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244 | (5) |
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Special Differential Subordinations |
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Conditions for Special Subclasses of Starlike Functions |
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249 | (20) |
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Simple Conditions for Starlikeness and Convexity |
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269 | (15) |
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On a Theorem of Robertson |
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284 | (5) |
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Subordination by Convex Functions |
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289 | (3) |
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Functions with Bounded Turning and Starlike Functions |
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292 | (21) |
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Functions Starlike with Respect to Symmetric Points |
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313 | (6) |
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Higher Order Differential Subordinations |
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319 | (3) |
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Third-Order Differential Subordinations |
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322 | (12) |
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The Euler Nth-Order Differential Subordination |
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334 | (7) |
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Differential Subordinations of Several Complex Variables |
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341 | (6) |
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Extensions of the Fundamental Lemma |
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347 | (21) |
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Dominants and Admissible Functions in Cn |
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368 | (5) |
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Differential Subordinations in Cn |
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373 | (6) |
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Applications of Differential Subordinations in Other Fields |
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379 | (3) |
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382 | (15) |
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Differential Subordinations in the Upper Half-Plane |
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397 | (11) |
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Extensions to Banach Spaces |
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408 | (7) |
| Appendix Convexity of Bernoulli Functions |
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415 | (6) |
| Bibliography |
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421 | (28) |
| List of Symbols |
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449 | (6) |
| Index |
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455 | |
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