A new subclass of bi-univalent functions associated with q-Chebychev polynomial

D, Kavitha; Dhanalakshmi, K.; Manikandan, P.

doi:10.22075/ijnaa.2022.28252.3845

A new subclass of bi-univalent functions associated with q-Chebychev polynomial

Document Type : Research Paper

Authors

Kavitha D ¹

K. Dhanalakshmi ²

P. Manikandan ³

¹ Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai, 605108, Tamilnadu, India

² PG & Research Department of Mathematics, Theivanai Ammal College for Women (Autonomous), Villupuram, 605602, Tamilnadu, India

³ Department of Mathematics, Anjalai Ammal Mahalingam Engineering College, Kovilvenni, 614403, Tamilnadu, India

10.22075/ijnaa.2022.28252.3845

Abstract

In this article, using the concept of q-analogue, we define a new class of analytic functions associated with Chebyshev polynomial of second kind. Then with the help of symmetric q-Chebyshev polynomial, we introduce and estimating first two Maclaurin coefficients for new subclasses of analytic functions. Also as application of the results, we estimate the relevant connection to the famous classical Fekete- Szegö inequality belonging to the class $\tilde{S}_{\Sigma}^{q}(\lambda,\gamma,s).$

Keywords

Univalent functions

Subordination

q-derivative

q-Chebyshev polynomial and Fekete-Szegö inequality