A Study on Subclasses of Harmonic Univalent Functions

Abstract

Harmonic univalent functions constitute an essential branch of the theory of geometric functions, extending the classical theory of analytic functions. Recent studies have focused on constructing new subclasses of harmonic mappings through operator-based approaches, which allow a systematic analysis of their geometric behavior. In this work, we obtain sufficient criteria of the harmonic function classes S_H^k (m,δ,β,λ,α) and C_H^k (m,δ,β,λ,α) corresponding to starlike and convex harmonic mappings associated with k-symmetric points. Moreover, necessary conditions characterizing the membership of a function f in the subclasses TS_H^k (m,δ,β,λ,α) and TC_H^k (m,δ,β,λ,α) are established. Finally, explicit growth inequalities are obtained for functions in TS_H^k (m,δ,β,λ,α).