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

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  • Serkan Çakmak
  • Sibel Yalçın

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.

Suggested Citation

  • Serkan Çakmak & Sibel Yalçın, 2026. "q-Poisson and q-Pascal Distribution Series for Analytic Function Classes," Journal of Mathematics, Hindawi, vol. 2026, pages 1-14, June.
    • Handle: RePEc:hin:jjmath:9345508
    DOI: 10.1155/jom/9345508
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