2023

DOI: 10.3390/math11040805

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Some Functionals and Approximation Operators Associated with a Family of Discrete Probability Distributions

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H. M. Srivástava

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Abstract: A certain discrete probability distribution was considered in ["A discrete probability distribution and some applications", Mediterr. J. Math., 2023]. Its basic properties were investigated and some applications were presented. We now embed this distribution into a family of discrete distributions depending on two parameters and investigate the properties of the new distributions.

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Cited by 4 publications

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Stabilities of multiplicative inverse quadratic functional equations arising from Pythagorean means

Senthil Kumar,

Dutta,

Shanmugam

et al. 2023

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In this article, we propose advanced multiplicative inverse quadratic functional equations involving arguments in rational form. The motivation to introduce these functional equations is due to inverse square law arising in gravity, electricity and radiation. We obtain their solutions and prove their stabilities in the restricted domain and non-Archimedean fields. Moreover, we provide a suitable counterexample for the failure of stability result when critical case arises. We elucidate these equations with Pythagorean means.

Stabilities of multiplicative inverse quadratic functional equations arising from Pythagorean means

Senthil Kumar,

Dutta,

Shanmugam

et al. 2023

View full text Add to dashboard Cite

In this article, we propose advanced multiplicative inverse quadratic functional equations involving arguments in rational form. The motivation to introduce these functional equations is due to inverse square law arising in gravity, electricity and radiation. We obtain their solutions and prove their stabilities in the restricted domain and non-Archimedean fields. Moreover, we provide a suitable counterexample for the failure of stability result when critical case arises. We elucidate these equations with Pythagorean means.

Bivariate Lupaş-Durrmeyer type operators involving Pólya distribution

Yadav,

Mohiuddine,

Kajla

et al. 2023

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Approximation results for the operators involving beta function and the Boas-Buck-Sheffer polynomials

Güngör,

Çekim,

Özarslan

2024

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In this study, we consider a sequence of linear positive operators involving the beta function and the Boas-Buck-Sheffer polynomials, and compute the convergence error of these operators using the first and second modulus of continuities. We give approximation properties in weighted space and we give a global error estimate in Lipschitz type space. We also construct a sequence of bivariate extensions of these operators and give the rate of convergence using the partial and full modulus of continuities. In addition, some examples, including graphs, are given for one- and two-variable functions to visually illustrate convergence to a function.

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