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 -calculus, we develop a new generalized symmetric -difference operator of convolution type, which is applicable in the domain . 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 to belong to the class , examining the sufficiency conditions for to satisfy these properties.

Study of quantum calculus for a new subclass of bi-univalent functions associated with the cardioid domain.

In this article, we make use of the concepts of subordination and the -calculus theory to analyze a new class of analytic bi-univalent functions associated to the cardioid domain. Our main focus is to derive a sharp inequality for a newly defined class of analytic and bi-univalent functions in the open unit disc . We explore the bounds of initial coefficients, Fekete-Szegö type problems, and coefficient inequalities for newly established families.