Studies on certain coefficient estimates for some new subclasses of analytic functions

Abstract

Chapter one consist of elementary concepts related to the entire thesis. The well known and important subclasses of univalent functions and multivalent functions such as starlike function, convex function and close-to-convex functions were defined. The related results of such classes were stated. Motivated by the earlier work of Ramachandran et al.(2018), the new subclass of close-to-convex function of order a associated with the Error function is defined. The result of Fekete Szeg¨o inequality and sharp bounds also determined. Also, the subclass of close-to-convex function of complex order with respect to the S and#728; al and#728; agean differential operator is defined and the new results are obtained. Let f 2 Ap, the generalized subclasses of starlike and convex function correspondence with the differential operator is defined. In addition of this, the new subclass of multivalent function associated with the non-Bazilevi and#711; c function is also defined. The classical Fekete Szeg ¨ o problem is investigated for these new subclasses. Using the theory of quasi-subordination, the coefficient bounds and the Fekete Szeg¨o results are calculated. A function f 2 A is said to be bi-univalent in U if both f (z) and f 0 (z) are univalent in U: The class of bi-univalent function is denoted by S. The initial coefficient estimates ja2j and ja3j for the new subclasses of analytic functions are defined by the S and#728; al and#728; agean operator using quasi-subordination is derived newline