PARTIAL SUMS OF MEROMORPHIC FUNCTIONS LINKED WITH q- DIFFERENTIAL OPERATOR

The paper presents the introduction of a novel linear differential operator for meromorphic functions associated with q- calculus. By means of this operator, a new subclass of meromorphic functions is defined and investigated in detail. The study focuses on deriving sufficient conditions that guarantee membership in this subclass and on establishing several analytic and geometric properties of the associated functions. Furthermore, the behavior of functions in the defined subclass is examined through the ratios of meromorphic functions to their sequences of partial sums. Various results describing these ratios are obtained, highlighting convergence and structural features. The findings enrich the theory of meromorphic functions and demonstrate the effectiveness of q - calculus-based operators in function theory.