Study of some properties in the theory of univalent functions. Univalent and multivalent functions with some applications

      Аннотация: In this study, we have studied a new subclass of meromorphic univalent functions with positive coefficients defined by Ruscheweyh derivative and here, we discuss several geometric properties, like, coefficient inequality, distortion and growth bounds, extreme points, arithmetic mean, convex linear combinations, region of univalency, in particular, starlikeness and convexity, also we have obtained Hadamard product and neighborhoods on our class. We have also introduced a class of univalent functions with negative coefficients defined by Hadamard product with Rafid - Operator. We obtain various properties, like, coefficient bounds, extreme points, radius of close – to – convexity and integral representation for , we have also obtained inclusive properties of the class and result by applying integral operator. In continuity of our work, we deals with new classes of starlike and convexity properties for Gussain hypergeometric functions.

Ключевые слова: univalent functions, integral operator, Rafid operator, multivalent functions