Applications of Generalized Mersenne Polynomials to a General Subclass of Bi-Bazilevič-Type Functions - Magesh, N.; Raju , D. S.; Tejas, N. S. (Communications in Mathematics and Applications, 2025)
This paper introduces a new subclass of generalized bi-Bazilevič-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.
Keywords: Bi-univalent functions; Bi-Bazileviˇc functions; Bi-starlike and Bi-convex functions; Fekete-Szegö inequality; Generalized Mersenne polynomials