A New Subclass of Analytic Functions Involving the (p, q)--Poisson Distribution Series
Mathematics, vol.14, no.12, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 14 Issue: 12
- Publication Date: 2026
- Doi Number: 10.3390/math14122029
- Journal Name: Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: (p, q)-derivative, (p, q)-Poisson distribution series, analytic function, coefficient estimate, Geometric Function Theory, Poisson distribution
- Istanbul Gelisim University Affiliated: Yes
Abstract
In this paper, we introduce and investigate a new subclass (Formula presented.) of analytic functions defined by the (Formula presented.) -derivative in the setting of Geometric Function Theory. This class extends the classical subclass (Formula presented.) and reduces to it when the parameters (Formula presented.) and (Formula presented.) tend to (Formula presented.). By means of coefficient estimates, we obtain a sufficient condition for the general class and a necessary and sufficient condition for the corresponding negative-coefficient subclass. These results are then applied to the (Formula presented.) -Poisson distribution series and to a related linear operator. The graphical analysis included in the final section illustrates the geometric behavior of the introduced functions and highlights the effects of the parameters.