<i>q</i>-Poisson and <i>q</i>-Pascal Distribution Series for Analytic Function Classes
JOURNAL OF MATHEMATICS, vol.2026, no.1, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 2026 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1155/jom/9345508
- Journal Name: JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Bursa Uludag University Affiliated: Yes
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.