Coefficient Estimates for a Subclass of Bi-univalent Functions Defined by Sălăgean Type q-Calculus Operator

Prakash Namdeo Kamble; Mallikarjun Gurullingappa Shrigan

doi:10.5666/KMJ.2018.58.4.677

Articles

Kyungpook Mathematical Journal 2018; 58(4): 677-688

Published online December 31, 2018

Coefficient Estimates for a Subclass of Bi-univalent Functions Defined by Sălăgean Type q-Calculus Operator

Prakash Namdeo Kamble, Mallikarjun Gurullingappa Shrigan^∗

Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India
e-mail : kamble.prakash69@gmail.com

Department of Mathematics, Dr. D Y Patil School of Engineering and Technology, Pune 412205, India
e-mail : mgshrigan@gmail.com

Received: March 7, 2018; Revised: September 25, 2018; Accepted: October 2, 2018

Abstract

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Abstract

In this paper, we introduce and investigate a new subclass of bi-univalent functions defined by Sălăgean q-calculus operator in the open disk . For functions belonging to the subclass, we obtain estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃|. Some consequences of the main results are also observed.

Keywords: analytic functions, bi-univalent functions, coefficient bounds, Sălăgean q-differential operator , Sălăgean derivative.