Coefficient Estimates for a Subclass of Bi-univalent Functions Associated with Symmetric q-derivative Operator by Means of the Gegenbauer Polynomials

Ala Amourah; Basem Aref Frasin; Tariq Al-Hawary

doi:10.5666/KMJ.2022.62.2.257

Article

Kyungpook Mathematical Journal 2022; 62(2): 257-269

Published online June 30, 2022

Coefficient Estimates for a Subclass of Bi-univalent Functions Associated with Symmetric q-derivative Operator by Means of the Gegenbauer Polynomials

Ala Amourah, Basem Aref Frasin^*, Tariq Al-Hawary

Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid, Jordan
e-mail : alaammour@yahoo.com

Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq, Jordan
e-mail : bafrasin@yahoo.com

Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan
e-mail : tariq_amh@bau.edu.jo

Received: July 3, 2021; Revised: November 5, 2021; Accepted: November 16, 2021

Abstract

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Abstract

In the present paper, a subclass of analytic and bi-univalent functions is defined using a symmetric q-derivative operator by means of Gegenbauer polynomials. Coefficients bounds for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szegö problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

Keywords: Gegenbauer polynomials, bi-univalent functions, analytic functions, Fekete-Szegö, problem