Geometric applications for meromorphic functions involving $\mathfrak{q}$-linear operators

This paper investigated the $\mathfrak{q}$-analogue of the multiplier-Ruscheweyh operator acting on meromorphic analytic functions, denoted by ${\mathfrak{D}}_{\mathfrak{q},\epsilon }^r(\varkappa ,\varrho ).$ By applying tools from $\mathfrak{q}$-calculus together with the principle of subordination, we developed several analytical results that deepened the understanding of geometric function theory (GFT) in the setting of meromorphic functions. The study focused on constructing new subclasses of meromorphic univalent functions associated with the operator ${\mathfrak{D}}_{\mathfrak{q},\epsilon }^r(\varkappa ,\varrho ),$ characterized by $\mathfrak{q}$-starlikeness, $\mathfrak{q}$-convexity, and related geometric classes. Various inclusion relationships, differential inequalities, and integral preservation properties were examined to establish the structural behavior of these families of functions. The findings generalized and unified several existing results in the literature concerning different operators and extended their applications to broader contexts within meromorphic function theory with $\mathfrak{q}$-calculus operator.