q-Poisson and q-Pascal Distribution Series for Analytic Function Classes

Serkan Çakmak and Sibel Yalçın

Journal of Mathematics, 2026, vol. 2026, 1-14

Abstract: In this paper, we study analytic function classes defined by the q-derivative and convolution operators generated by discrete q-distributions. We first consider coefficient conditions for the class determined by a q-derivative inequality and its negative-coefficient subclass. We then investigate the q-Poisson and q-Pascal distribution series and derive explicit sufficient conditions for their membership in this class. In addition, we establish inclusion results for convolutions with q-starlike and q-convex functions and prove corresponding self-inclusion properties. Numerical examples are provided to verify the theoretical results. These results connect distribution-based convolution operators with q-derivative inequalities in geometric function theory.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9345508

DOI: 10.1155/jom/9345508

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