A Class of p-Valent Close-to-Convex Functions Defined Using Gegenbauer Polynomials

Abstract

A new class of p-valent close-to-convex functions is introduced in this paper, which is defined using Gegenbauer Polynomials within the open unit disk D. This investigation sheds light on the properties and behaviors of these p-valent close-to-convex functions, providing estimations for the modulus of the coefficients a_p+1 and a_p+2, with p being a natural number, for functions falling under this particular class. Additionally, this paper also investigates the classical Fekete-Szegö functional problem for functions f that are part of the aforementioned class.