On certain subclasses of analytic univalent function associated with special functions

Abstract

The first chapter consists of general introduction to the subject newlinewhich are compatible to the entire thesis The basic concepts like univalence newlinestarlikeness convexity and its related results were recalled Renowned and newlineprominent properties of several subclasses of analytic functions are stated in newlinethe form of theorems without proof newlineIn the second chapter a new class of convex and starlike functions newlinenamely q convex error functions and q starlike error functions were introduced newlineand discussed its coefficient estimates through quasi subordination in conical newlinedomain Sharp bound of the Fekete Szeg o Coefficient for the general class newlineof spirallike functions of universally prestarlike functions associated with qth newlinederivative operator using m th root transformation which is involved in conical newlineregions are also discussed in this chapter newlineThird chapter contributes the Fekete Szeg o inequality for generalized newlineclass of analytic functions of complex order with q difference operator through newlinesubordination newlineFourth chapter furnish some conditions on the parameters involved newlinein generalized hypergeometric function and derived the mapping properties newlineof various subclasses of starlike and uniformly convex functions defined newlinethrough a generalized hypergeometric function The mapping properties of newlinevarious subclasses of k-uniformly convex and starlike functions involving newlinethe generalized Fox Wright function were discussed extensively The results newlineobtained in this chapter can be deduced to earlier known results and new results newlinefor suitable choices of the parameter newline newline