Abstract
The main contribution of this article is to define a family of starlike functions associated with a cosine hyperbolic function. We investigate convolution conditions, integral preserving properties, and coefficient sufficiency criteria for this family. We also study the differential subordinations problems which relate the Janowski and cosine hyperbolic functions. Furthermore, we use these results to obtain sufficient conditions for starlike functions connected with cosine hyperbolic function.
Highlights
Introduction and DefinitionsThe aims of this particular section is to include some basic notions about the Geometric FunctionTheory that will help to understand our key findings in a clear way
The set S ⊂ A describes the family of all univalent functions which is define here by the following set builder form: S = {q ∈ A : q is univalent in D}
Analytic functions are classified into various families based on geometry of image domains
Summary
Theory that will help to understand our key findings in a clear way In this regards, first we start to define the most basic family A which consists of holomorphic (or analytic) functions in D =. Analytic functions are classified into various families based on geometry of image domains. 1+ M are its different end points of the diameter This familiar function is recognized as Janowski function [2]. Some interesting problems such as convolution properties, coefficients inequalities, sufficient conditions, subordinates results, and integral preserving were discussed recently in [3,4,5,6,7].
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