Some Application on Subclass of Meromorphic Functions Associated with q-Analogue Multiplier Operator

Abstract

In this paper, we introduce a new linear operator D^r_q(λ , ℓ)f(ζ ) and employ it to define a q-analogue of a differential operator acting on a newly developed subclass of meromorphic functions in the punctured unit disk. The subclass, denoted Σ_q^{∗, r} (Θ, λ , ℓ), is examined comprehensively, and several of its key analytic and geometric properties are established. Specifically, we derive coefficient conditions for functions in this class and study convolution properties, closure results, convex combination criteria, and the interaction of the class with the q-Bernardi integral operator. Moreover, we address and resolve the neighborhoods problem associated with this subclass. These findings offer new insights into meromorphic function theory within the framework of q-calculus operators and underscore the potential for further development of operator generated function classes in geometric function theory.