A q-Analogue of Janowski-Type Analytic Functions and Their Geometric Properties

Motivated by recent progress in the q-calculus and its applications to geometric function theory, this paper introduces a new subclass of normalized analytic functions defined through the Jackson q-derivative and a Janowski-type subordination condition. The proposed class extends several well-known families of starlike and convex functions by incorporating the q-parameter, allowing a more flexible geometric interpretation. We investigate fundamental properties of this class by establishing convolution characterizations and deriving necessary and sufficient membership conditions. In addition, sharp bounds for the initial Taylor coefficients are obtained, and the associated Fekete–Szegő functional is examined. Various special cases are discussed to illustrate the generality of the results. It is also shown that the classical results are recovered naturally as the parameter q → 1 − , confirming the consistency of the proposed q-analogue with the existing theory.