CHEBYSHEV POLYNOMIALS AND BI-UNIVALENT FUNCTIONS ASSOCIATING WITH $q$-DERIVATIVE OPERATOR

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 31

Volume : 20 , Issue : 2
DOI: https://doi.org/10.56827/SEAJMMS.2024.2002.11
Author :
P. Nandini (Department of Mathematics, JSS Academy of Technical Education, Srinivaspura, Bengaluru - 560060, INDIA)
S. Latha (Department of Mathematics, JSS Academy of Technical Education, Srinivaspura, Bengaluru - 560060, INDIA)
G. Murugusundaramoorthy (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (Deemed to be University), Vellore 632014, Tamil Nadu, INDIA)

Abstract

In this paper, we introduce and investigate a new subclass of Bi-univalent functions defined in the open unit disk, associated with Chebyshev polynomials by applying $q$-derivative operator. Furthermore, We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class and also we obtain an estimation for Fekete-Szeg$\ddot{o}$ problem for this class.

Keywords and Phrases

Analytic functions, Univalent and Bi-univalent functions, Fekete-Szeg$\ddot{o}$ inequality, Chebyshev polynomials and $q$-derivative operator.

A.M.S. subject classification

30C45, 30C50.

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