Some Properties of Multivalent Analytic Starlike Function Subordinated with Cosine Hyperbolic Function

Abstract

Abdullah Alotaibi defined a starlike function connected with a cosine hyperbolic function in the year 2020. We establish some appropriate conditions for several features of multivalent analytic starlike function subordinated with cosine hyperbolic function in this article. We determine conditions on α are subordinated by Janowski function. We acquire some suitable conditions by selecting specific values for functions we get some adequate conditions for multivalent starlik function related with cosine hyperbolic. Over the last decade, starlike functions have grown in popularity in both literature and application. Our goal in this work is look at some practical challenges with q-starlike functions. Moreover, we will show that the class described in this research, as well as the results gained, generalizes numerous previously published papers. We need to add some fundamental Geometric function theory literature here to comprehend the notions employed in our work in a straightforward way. To do so, we'll start with the notation, which signifies the class of holomorphic or analytic functions in the holomorphic or analytic functions. Then the relationships must be stable. In addition, all univalent functions will belong to the subfamily. Furthermore, the possibility of subjections between analytic functions and, as shown by, as; the functions, are related by the connection of subjection, if there exists an analytic function with restrictions and such that in addition, if the function is in, we get The aim of this paper is to define a family of multivalent q-starlike functions associated with circular domains and to study some of its useful properties of multivalent analytic functions subordinated cosine hyperbolic function.