Some geometrical and analytical properties for certain classes of multivalent starlike functions

Abstract

The main objective of this research is to obtain several analytic and geometric properties of analytic and multivalent (𝑝-valent) starlike functions defined in the open unit disk associated with certain linear operator by introducing certain classes and deriving some properties. In this thesis, a wide class of problems is investigated. First, Fekete-Szegӧ problems for functions belonging to some classes of 𝑝-valent starlike functions are solved. In addition, numerous starlikeness and convexity conditions of 𝑝-valent functions are obtained. Finally, certain classes of 𝑝-valent starlike functions with negative coefficients are defined, in obtaining, coefficient bounds, distortion properties, convolution properties, closure properties, extreme points, radius of close-to-convexity, radius of starlikeness, radius of convexity, class-preserving integral operators and integral means inequalities