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

Khan, Mohammad Faisal; AbaOud, Mohammed

doi:10.3390/fractalfract7030270

Open AccessArticle

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

by

Mohammad Faisal Khan

^1,*

and

Mohammed AbaOud

²

¹

Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia

²

Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia

^*

Author to whom correspondence should be addressed.

Fractal Fract. 2023, 7(3), 270; https://doi.org/10.3390/fractalfract7030270

Submission received: 21 February 2023 / Revised: 13 March 2023 / Accepted: 17 March 2023 / Published: 18 March 2023

(This article belongs to the Special Issue Fractional Calculus and Hypergeometric Functions in Complex Analysis)

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Abstract

This work examines a new subclass of generalized bi-subordinate functions of complex order

γ

connected to the q-difference operator. We obtain the upper bounds

ρ_{m}

for generalized bi-subordinate functions of complex order

γ

using the Faber polynomial expansion technique. Additionally, we find coefficient bounds

|ρ_{2}|

and Feke–Sezgo problems

|ρ_{3} - ρ_{2}^{2}|

for 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.

Keywords: quantum (or q-) calculus; analytic functions; univalent functions; q-derivative operator; convex functions; starlike functions; bi-univalent functions; Faber polynomial expansion

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MDPI and ACS Style

Khan, M.F.; AbaOud, M. Some New Applications of the Faber Polynomial Expansion Method for Generalized Bi-Subordinate Functions of Complex Order γ Defined by q-Calculus. Fractal Fract. 2023, 7, 270. https://doi.org/10.3390/fractalfract7030270

AMA Style

Khan MF, AbaOud M. 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. 2023; 7(3):270. https://doi.org/10.3390/fractalfract7030270

Chicago/Turabian Style

Khan, Mohammad Faisal, and Mohammed AbaOud. 2023. "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 7, no. 3: 270. https://doi.org/10.3390/fractalfract7030270

APA Style

Khan, M. F., & AbaOud, M. (2023). 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, 7(3), 270. https://doi.org/10.3390/fractalfract7030270

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

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