On subclasses of close-to-convex functions and related functions

Abstract

Denote by S the class of functions f which are analytic and univalent in the unit disc D = { z ·ll < 1} in the complex

I plane C and normalized so that f(0) = f (0) - 1 = 0.

denotes the class of analytic functions

Let P

co h(z) = 1 + 7 n= 1

which have a positive real part in D.

C z n n

The subclasses of S consisting of functions which are convex' convex of order a, starlike starlike of order a, close-to- convex and close-to- convex of order a,are denoted by C, C,, S•,, K and K,, respectively. Such that, for a = 0, we

have C = C , S • = S •

and K = K 0 0 0

They are related by the inclusion relations

cc s cKcs, and C~<S% (see [13] I [21] I [28] / [38]) •

In, Abdel Gwad and Thomas [2] are considered a certain class

J of analytic functions for a subclass Jin K, such that J c K.

In this thesis we develop some of the basic properties of functions, a subclass J~ in , such that, < a·

The aim of the thesis is to define and study some classes of analytic functions in D.

This it consists rnainaly of three chapters.

In the first chapter, we recalled the known results for the

• various subclasses of Sare listed. It consists of three sections: