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

Muhammad Azam,Naseer Ullah

doi:10.11648/j.ijamtp.20210703.13

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.

Highlights

To understand in a clear way the notions used in our results, we need to add here some basic literature of Geometric function theory
Using the idea of multivalent functions, we introduce the class SI∗D of multivalent starlike functions associated with cosine hyperbolic function and as given below:
In the current exploration paper, we inspected a few fascinating traits of starlike functions related with the cosine hyperbolic function

Summary

Introduction

To understand in a clear way the notions used in our results, we need to add here some basic literature of Geometric function theory. The function ψ κ = 1 + Åκ ⁄ 1 + Bκ , −1 ≤ B < Å ≤ 1 maps C onto the disc on the right half plane with center on the real axis and diameter end points *F and -F. The image of the function ψ κ = cash κ shows that the picture space is limited by the right half of the cosine hyperbolic [25]. Subordinated with Cosine Hyperbolic Function studied in [23]. We accept that the accompanying limitations otherwise we will state it where different

Adequate Conditions Associated with Cosh

Conclusions