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

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 $E^{⁎}=\{\tau :\tau \in C\text{and}0<\left|\tau \right|<\infty \}$ . 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 $M{S}_H^{P,R}(q,q^{-1})$ , examining the sufficiency conditions for F to satisfy these properties. Moreover, we examine key geometric properties of the function F in the class $M{S}_{\bar{H}}^{P,R}(q,q^{-1})$ , including the distortion bound, convex combinations, the extreme point theorem, and weighted mean estimates.