Applications of Generalized Mersenne Polynomials to a General Subclass of Bi-Bazilevic-Type Functions

Authors

Keywords:

Bi-univalent functions, Bi-Bazilevic functions, Bi-Starlike and Bi-Convex functions, Fekete-Szego inequality, Generalized Mersenne polynomials

Abstract

This paper introduces a new subclass of generalized bi-Bazilevic-type functions associated with the generating function of generalized Mersenne polynomials, which encompasses several eminent and widely studied subclasses, such as bi-starlike and bi-convex functions. The use of generalized Mersenne polynomials highlights the applicability of special polynomials in geometric function theory. By applying the generating function of the generalized Mersenne polynomials, we derive coefficient bounds for the initial Taylor–Maclaurin coefficients and provide estimates for the Fekete–Szego inequality. Furthermore, we discuss several corollaries by specifying particular choices of the parameters.

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Published

19-02-2026

How to Cite

N Magesh, D S Raju, & N S Tejas. (2026). Applications of Generalized Mersenne Polynomials to a General Subclass of Bi-Bazilevic-Type Functions . Communications in Mathematics and Applications, 16(3). Retrieved from https://www.rgnpublications.com/journals/index.php/cma/article/view/3313

Issue

Vol. 16 No. 3 (2025)

Section

Research Article

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