Department of Pure Mathematics

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Numerical Solution of Ordinary Differential Equations

(University of Khartoum, 2013) Ebraheem, Abdulla ; Abdelgader, Hind ; Abdalazeem, Samah
A Study of Certain Classes of Univalent and Related Functions.

(UOFK, 1981) Ahuja, Adam Prakash

In the present thesis, an attempt has been made to unify various subclasses of analytic functions which are spiral like, close to convex special close- to - convex, close to star, meromotphically close- to – star, close – to – spiral like and starlike with negative coefficients by introducing the concept of type for each of these classes. An analogous unified approach has also been made for the Robertson, and close - to – Robertson functions. Thus we study several subclasses of analytic functions which not only unify a number of classes previously studied: but also give rise to many new subclasses of univalent and related functions. Classified into nine chapters, this thesis starts with a brief survey of the subject in general: and then basic concepts and results are presented in chapter 1. The chapters 11 to v11 contain the results of our investigations on a study of certain classes of univalent and related functions with general coefficients. The remaining chapters VII, VIII and IX deal with the study of analytic functions with negative coefficients.