Coefficient bounds of a class of function defined by the Gegenbauer-Horadam polynomial
Fixed Point Methods and Optimization, Volume 2, Issue 2, August 2025, Pages 117–126
OLUWASEYI DAVID OLAWUMI
Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin, Nigeria
OLUBUNMI ABIDEMI FADIPE-JOSEPH
Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin, Nigeria
Abstract
Geometric Function Theory, a branch of complex analysis, explores the geometric properties of analytic functions. Researchers in Geometric Function Theory investigate coefficient problems, radius problems, growth and distortion for different classes of analytic functions. This research considered geometric properties and behavior of some polynomials. Gegenbauer and Horadam polynomials are special polynomials with various applications. A new polynomial called Gegenbauer-Horadam (G-H) polynomial was introduced. The polynomial generalizes other polynomials; like the Horadam polynomial, Gegenbauer polynomial, Fibonacci polynomial, Chebyshev polynomial of the first and second kind, Pell polynomial, Lucas polynomial, Pell-Lucas polynomial, and many more. The significance of the Gegenbauer-Horadam polynomial lies in its ability to generalize and connect various polynomials, making it a valuable tool for researchers. Subordination principle was used to define the new class of analytic functions, \(g_{\alpha,\beta}(z)\). Coefficient bounds, Fekete-Szegö functional and other functionals were established. The study finds applications in related fields such as physics, engineering, signal processing, and number theory.
Cite this Article as
Oluwaseyi David Olawumi and Olubunmi Abidemi Fadipe-Joseph, Coefficient bounds of a class of function defined by the Gegenbauer-Horadam polynomial, Fixed Point Methods and Optimization, 2(2), 117–126, 2025