Monotone coefficients of univalent harmonic functions with applications to special functions

Abstract

The manuscript intends to establish monotone conditions on the coefficients of the power series f(z)=z+∑<inf>n=2</inf>∞a<inf>n</inf>zn+∑<inf>n=2</inf>∞b<inf>n</inf>zn‾ to ensure its close-to-convexity (univalency) in the unit disk. We apply these coefficient conditions to illustrate the univalence characteristics of several important non-trivial harmonic functions associated with Gaussian hypergeometric functions. In our investigation, we employ sufficient conditions for a function to be close-to-convex in the unit disk. © 2025 Elsevier B.V., All rights reserved.