Some New Applications of the q -Analogous of Differential and Integral Operators for New Subclasses of q -Starlike and q -Convex Functions

Fractal and Fractional

article

Suha B. Al-Shaikh¹  Ahmad A. Abubaker¹  Khaled Matarneh¹  Mohammad Faisal Khan² 

[1] Faculty of Computer Studies, Arab Open University;Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University

关键词: analytic functions;    convolution;    quantum (or q-) calculus;    q-difference operator;    q-integral operator;    q-starlike and q-convex functions;    differential subordination05A30;    30C45;    11B65;    47B38;   

DOI  :  10.3390/fractalfract7050411

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

In the geometric function theory of complex analysis, the investigation of the geometric properties of analytic functions using q-analogues of differential and integral operators is an important area of study, offering powerful tools for applications in numerical analysis and the solution of differential equations. Many topics, including complex analysis, hypergeometric series, and particle physics, have been generalized in q-calculus. In this study, first of all, we define the q-analogues of a differential operator (DRλ , q m , n) by using the basic idea of q-calculus and the definition of convolution. Additionally, using the newly constructed operator (DRλ , q m , n), we establish the q-analogues of two new integral operators (Fλ ,γ1 ,γ2 , …γ lm , n , qand Gλ ,γ1 ,γ2 , …γ lm , n , q ), and by employing these operators, new subclasses of the q-starlike and q-convex functions are defined. Sufficient conditions for the functions (f) that belong to the newly defined classes are investigated. Additionally, certain subordination findings for the differential operator (DRλ , q m , n) and novel geometric characteristics of the q-analogues of the integral operators in these classes are also obtained. Our results are generalizations of results that were previously proven in the literature.

【 授权许可】

CC BY