New subclass of meromorphic harmonic functions defined by symmetric q-calculus and domain of Janowski functions

Abstract

In this article, by applying the convolution principle and symmetric q-calculus, we develop a new generalized symmetric q-difference operator of convolution type, which is applicable in the domain E⁎={τ:τ∈C and 0<|τ|<∞}. Utilizing this operator, we construct, analyze, and evaluate two new sets of meromorphically harmonic functions in the Janowski domain. Furthermore, we investigate the convolution properties and necessary conditions for a function F to belong to the class MSHP,R(q,q−1), examining the sufficiency conditions for F to satisfy these properties. Moreover, we examine key geometric properties of the function F in the class MSH‾P,R(q,q−1), including the distortion bound, convex combinations, the extreme point theorem, and weighted mean estimates.