SOME PROPERTIES OF ANALYTIC FUNCTIONS ASSOCIATED WITH HURWITZ-ZETA FUNCTION

The study of the geometric properties of analytic functions and their numerous applications across a variety of mathematical fields, including fractional calculus, probability distributions, and special functions, has drawn significant attention to Geometric Function Theory (GFT), one of the most prominent branches of complex analysis, in recent years. In this paper, we introduce a new subclass of uniformly convex functions with negative coefficients, defined in terms of the Hurwitz-Zeta function. We obtain the coefficient bounds, convex linear combinations, radii of close-to-convexity, starlikeness and integral means inequality for functions belonging to the class. Furthermore, we obtain neighbourhood results for this class.