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


ÇAKMAK S., YALÇIN TOKGÖZ S.

Journal of Mathematics, cilt.2026, sa.1, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2026 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1155/jom/9345508
  • Dergi Adı: Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: coefficient inequalities, convolution operator, q-convex functions, q-derivative, q-Pascal distribution series, q-Poisson distribution series, q-starlike
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

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.