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Title: Extreme problems for certain classes of analytic functions
Author: Darus, M.
Awarding Body: University College of Swansea
Current Institution: Swansea University
Date of Award: 1995
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This thesis is concerned with extreme problems for certain classes of analytic functions. In many cases, the classes of functions considered form proper subclasses of the class S of normalised analytic functions which are univalent in the unit disc D. In Chapter 1, we present some definitions and known results which are required in subsequent chapters. In Chapter 2, we state some known results concerning the so-called Fekete-Szegö Theorem. We give some extensions and new results in the case of close-to-convex functions. Chapter 3 contains some miscellaneous Fekete-Szegö Theorems. In this chapter, we introduce a new class of analytic functions, which we call logarithmically convex. These functions are a natural analogue to the so-called α-convex functions, studied extensively over the last decade or so. Some extreme coefficient problems are solved for logarithmically convex functions. The final chapter deals with subordination. We apply a lemma of Miller and Mocanu to obtain a series of best possible subordination theorems when the super-ordinate function lies in a sector, rather than the usual half-plane. A consequence of one such result is that the logarithmically convex functions defined in Chapter 3 form a subset of the starlike functions and are thus univalent in D.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available