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

Authors

  • N. Magesh Post-Graduate and Research Department of Mathematics, Government Arts College for Men (affiliated to Periyar University), Krishnagiri 635001, Tamilnadu, India https://orcid.org/0000-0002-0764-8390
  • D. S. Raju Department of Mathematics, The National Institute of Engineering (affiliated to Visvesvaraya Technological University), Mysore 570008, Karnataka, India https://orcid.org/0009-0003-0696-6332
  • N. S. Tejas Department of Mathematics, The National Institute of Engineering (affiliated to Visvesvaraya Technological University), Mysore 570008, Karnataka, India https://orcid.org/0009-0009-4783-5092

DOI:

https://doi.org/10.26713/cma.v16i3.3313

Keywords:

Bi-univalent functions, Bi-Bazileviˇc functions, Bi-starlike and Bi-convex functions, Fekete-Szegö inequality, Generalized Mersenne polynomials

Abstract

This paper introduces a new subclass of generalized bi-Bazileviˇc-type functions which encompasses several eminent and widely studied subclasses, such as bi-starlike and bi-convex functions associated with the generating function of generalized Mersenne polynomials. 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-Szegö inequality. Furthermore, several corollaries are discussed by specifying particular parameter choices.

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Published

30-10-2025
CITATION

How to Cite

Magesh, N., Raju , D. S., & Tejas, N. S. (2025). Applications of Generalized Mersenne Polynomials to a General Subclass of Bi-Bazileviˇc-Type Functions. Communications in Mathematics and Applications, 16(3), 949–960. https://doi.org/10.26713/cma.v16i3.3313

Issue

Vol. 16 No. 3 (2025)

Section

Research Article

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