Some New Applications of the Faber Polynomial Expansion Method for Generalized Bi-Subordinate Functions of Complex Order γ Defined by q -Calculus

Fractal and Fractional

article

Mohammad Faisal Khan¹  Mohammed AbaOud² 

[1] Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University;Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University

关键词: quantum (or q-) calculus;    analytic functions;    univalent functions;    q-derivative operator;    convex functions;    starlike functions;    bi-univalent functions;    Faber polynomial expansion05A30;    30C45;    11B65;    47B38;   

DOI  :  10.3390/fractalfract7030270

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

This work examines a new subclass of generalized bi-subordinate functions of complex orderγconnected to the q-difference operator. We obtain the upper bounds ρ m for generalized bi-subordinate functions of complex orderγusing the Faber polynomial expansion technique. Additionally, we find coefficient boundsρ 2and Feke–Sezgo problemsρ 3−ρ22for the functions in the newly defined class, subject to gap series conditions. Using the Faber polynomial expansion method, we show some results that illustrate diverse uses of the Ruschewey q differential operator. The findings in this paper generalize those from previous efforts by a number of prior researchers.

【 授权许可】

CC BY