A New Subclass of Analytic Functions Involving the (p,q)-Derivative and Applications to (p,q)-Poisson Distribution Series

Yalçın, Sibel; Bayram, Hasan; Çakmak, Serkan

doi:10.3390/math14122029

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A New Subclass of Analytic Functions Involving the (p,q)-Derivative and Applications to (p,q)-Poisson Distribution Series

by

Sibel Yalçın

^1,*

,

Hasan Bayram

¹

and

Serkan Çakmak

²

¹

Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University, Bursa 16059, Türkiye

²

Management Information Systems Department, Faculty of Economics, Administrative and Social Sciences, Istanbul Gelisim University, Istanbul 34310, Türkiye

^*

Author to whom correspondence should be addressed.

Mathematics 2026, 14(12), 2029; https://doi.org/10.3390/math14122029

Submission received: 3 May 2026 / Revised: 26 May 2026 / Accepted: 5 June 2026 / Published: 6 June 2026

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions, 2nd Edition)

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Abstract

In this paper, we introduce and investigate a new subclass

A_{p, q} (λ, δ, η)

of analytic functions defined by the

(p, q)

-derivative in the setting of Geometric Function Theory. This class extends the classical subclass

G (λ, δ, η)

and reduces to it when the parameters

p

and

q

tend to

1^{-}

. 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

(p, q)

-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.

Keywords: analytic function; Geometric Function Theory; (p,q)-derivative; Poisson distribution; (p,q)-Poisson distribution series; coefficient estimate

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MDPI and ACS Style

Yalçın, S.; Bayram, H.; Çakmak, S. A New Subclass of Analytic Functions Involving the (p,q)-Derivative and Applications to (p,q)-Poisson Distribution Series. Mathematics 2026, 14, 2029. https://doi.org/10.3390/math14122029

AMA Style

Yalçın S, Bayram H, Çakmak S. A New Subclass of Analytic Functions Involving the (p,q)-Derivative and Applications to (p,q)-Poisson Distribution Series. Mathematics. 2026; 14(12):2029. https://doi.org/10.3390/math14122029

Chicago/Turabian Style

Yalçın, Sibel, Hasan Bayram, and Serkan Çakmak. 2026. "A New Subclass of Analytic Functions Involving the (p,q)-Derivative and Applications to (p,q)-Poisson Distribution Series" Mathematics 14, no. 12: 2029. https://doi.org/10.3390/math14122029

APA Style

Yalçın, S., Bayram, H., & Çakmak, S. (2026). A New Subclass of Analytic Functions Involving the (p,q)-Derivative and Applications to (p,q)-Poisson Distribution Series. Mathematics, 14(12), 2029. https://doi.org/10.3390/math14122029

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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A New Subclass of Analytic Functions Involving the (p,q)-Derivative and Applications to (p,q)-Poisson Distribution Series

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