Inclusion relations for some classes of analytic functions involving Pascal distribution series

Lashin, A. Y.; Badghaish, Abeer O.; Algethami, Badriah Maeed

doi:10.1186/s13660-022-02897-8

Cited by 2 publications

(1 citation statement)

References 15 publications

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“…Te authors in [18] discussed the concept of q-derivative and studied several inequalities of analytic functions by using the generalized Sǎlǎgean differential operator. On the other hand, Lashin et al in [19] discovered some inclusion relations of subclasses of analytic functions associated with the Pascal distribution probability.A random variable X with Poisson distribution takes the exponential probability that is given by…”

Section: Introductionmentioning

confidence: 99%

Inclusion and Neighborhood on a Multivalent q-Symmetric Function with Poisson Distribution Operators

Amini,

Al-Omari,

Suthar

2024

Journal of Mathematics

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In this paper, by using Poisson distribution probability, some characteristics of analytic multivalent q-symmetric starlike and q-symmetric convex functions of order η are examined. Then, by utilizing the Poisson distribution and the concept of the q-analogue Salagean integral operator, the p-valent convergence polynomial was introduced. Furthermore, a number of subclasses of analytic symmetric p-valent functions linked to novel polynomials are also deduced. After that, specific coefficient constraints are determined and symmetric δ,q-neighborhoods for p-valent functions are defined. In relation to symmetric δ,q-neighborhoods of q-symmetric p-valent functions formed by Poisson distributions, this paper presents new inclusion results. In addition, a detailed discussion of certain q-symmetric inequalities of analytic functions with negative coefficients is also provided.

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Section: Introductionmentioning

confidence: 99%

Inclusion and Neighborhood on a Multivalent q-Symmetric Function with Poisson Distribution Operators

Amini,

Al-Omari,

Suthar

2024

Journal of Mathematics

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show abstract

Inclusion Properties of p-Valent Functions Associated with Borel Distribution Functions

et al. 2023

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In this paper, we define a differential operator on an open unit disk Δ by using the novel Borel distribution (BD) operator and means of convolution. This operator is adopted to introduce new subclasses of p-valent functions through the principle of differential subordination, and we focus on some interesting inclusion relations of these classes. Additionally, some inclusion relations are derived by using the Bernardi integral operator. Moreover, relevant convolution results are established for a class of analytic functions on Δ, and other results of analytic univalent functions are derived in detail. This study provides a new perspective for developing p-univalent functions with BD and offers valuable understanding for further research in complex analysis.

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Inclusion relations for some classes of analytic functions involving Pascal distribution series

Abstract: In this article, we introduce and discuss some new subclasses of functions that are analytic in the open unit disc and involve the Pascal distribution series. Moreover, inclusion relations and integral preserving properties of these subclasses are determined.

Cited by 2 publications

References 15 publications

Inclusion and Neighborhood on a Multivalent q-Symmetric Function with Poisson Distribution Operators

Inclusion and Neighborhood on a Multivalent q-Symmetric Function with Poisson Distribution Operators

Inclusion Properties of p-Valent Functions Associated with Borel Distribution Functions

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