Study on new integral operators defined using confluent hypergeometric function

Abstract

Two new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function. It is proved that the new operators preserve certain classes of univalent functions, such as classes of starlike and convex functions, and that they extend starlikeness of order $\frac{1}{2}$ 1 2 and convexity of order $\frac{1}{2}$ 1 2 to starlikeness and convexity, respectively. For obtaining the original results, the method of admissible functions is used, and the results are also written as differential inequalities and interpreted using inclusion properties for certain subsets of the complex plane. The example provided shows an application of the original results.

Certain Integral Operators of Analytic Functions

“…The field of study involving differential and integral operators has been a constant research topic from the beginning of the field of study on analytic functions, with the first integral operator being introduced by Alexander in 1915 [1]. Differential and integral operators or combinations of those forms of operators are still emerging [2,3]. Sȃlȃgean and Ruscheweyh operators play a significant role in research, as can be exemplified by very recent papers, such as [4][5][6][7].…”

Study on the Criteria for Starlikeness in Integral Operators Involving Bessel Functions

“…Studies concerning the variants of differential subordination and superordiantion theories introduced in recent years as extensions named fuzzy differential subordination and superordination and strong differential subordination and superordination, respectively, could also be conducted on the operator F(z) defined in this paper. Such inspiring results can be seen in [18,26] for fuzzy differential subordination theory and for strong differential subordination and superordination theory in [27,28].…”

“…Additional motivation for the definition of the new generalized integral operator involving the Bessel function of the first kind is provided by the research, which involved other generalized integral operators [17,18], and by the compelling results recently made available concerning the geometric properties of integral operators defined pertaining to the Bessel function [19,20].…”

Coefficient Inequalities of q-Bi-Univalent Mappings Associated with q-Hyperbolic Tangent Function

“…In 1915, Alexander [1] introduced the first integral operator, this discovery played a crucial role in the examination of analytical functions. Since then, the main goal of current discovery in complex analysis (Geometric Function Theory) has revolved around this area, encompassing fractional derivative operators and derivatives that are often combined in various ways [2,3]. Recently published research, exemplified by [4], highlights the significance of integral fractional and differential operators in research.…”