A New Version of the Generalized Krätzel–Fox Integral Operators

Al‐Omari, Shrideh; Jumah, Ghalib; Al-Omari, J. F. M.; Saxena, Deepali

doi:10.3390/math6110222

Cited by 8 publications

(4 citation statements)

References 11 publications

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“…Moreover, the notion of primal is the dual structure of grill. Furthermore, some new studies have been revealed regarding primal topological spaces in [2,3,4,5] since the introduction of primal.…”

Section: Introductionmentioning

confidence: 99%

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

ÖZKOÇ,

KÖSTEL

2024

Preprint

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The main purpose of this paper is to introduce and study two new operators $(\cdot)_{R}^{\diamond}$ and $cl_{R}^{\diamond}(\cdot)$ via primal which is a new notion. We also show that the operator $cl_{R}^{\diamond}(\cdot)$ is a Kuratowski closure operator, while the operator $(\cdot)_{R}^{\diamond}$ is not. In addition, we prove that the topology on $X$, shown as $\tau_{R}^{\diamond}$, obtained by means of the operator $cl_{R}^{\diamond}(\cdot)$ is finer than $\tau_{\delta}$, where $\tau_{\delta}$ is the family of $\delta$-open subsets of a space $(X,\tau)$. Moreover, we not only obtain a base for the topology $\tau_{R}^{\diamond}$ but also prove many fundamental results concerning this new structure. Furthermore, we give many counterexamples related to our results. 2020 AMS Classifications: 54A05; 54B99; 54C60.

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Section: Introductionmentioning

confidence: 99%

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

ÖZKOÇ,

KÖSTEL

2024

Preprint

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“…Some of these functions were introduced to solve specific problems and some others were used to solve general problems. In recent years, generalized and multivariable forms of special functions of mathematical physics have also undergone significant evolutions (see [1][2][3][4][5][6][7][8][9][10][11][12] for more details). The theory of orthogonal polynomials and special functions is of intrinsic interest to many parts of mathematics.…”

Section: Introductionmentioning

confidence: 99%

Some Generalized Properties of Poly-Daehee Numbers and Polynomials Based on Apostol–Genocchi Polynomials

et al. 2022

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Numerous polynomial variations and their extensions have been explored extensively and found applications in a variety of research fields. The purpose of this research is to establish a unified class of Apostol–Genocchi polynomials based on poly-Daehee polynomials and to explore some of their features and identities. We investigate these polynomials via generating functions and deduce various identities, summation formulae, differential and integral formulas, implicit summation formulae, and several characterized generating functions for new numbers and polynomials. Finally, by using an operational version of Apostol–Genocchi polynomials, we derive some results in terms of new special polynomials. Due to the generic nature of the findings described here, they are used to reduce and generate certain known or novel formulae and identities for relatively simple polynomials and numbers.

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“…where (γ ) n is the Pochhammer symbol (see [21] p. 2 and pp. [4][5][6] and Γ (•) is the gamma function (see [21] Sect. 1.1), with the two auxiliary functions…”

Section: Definition 11 Wright Introduced the Classical Wright Functionmentioning

confidence: 99%

Computation of certain integral formulas involving generalized Wright function

et al. 2020

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The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms of the generalized hypergeometric function as well. Based on the main results, some integral formulas involving different special functions connected with the generalized Wright function are explicitly established as special cases for different values of the parameters. Moreover, a Gaussian quadrature formula has been used to compute the integrals and compare with the main results by using graphical representations.

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A New Version of the Generalized Krätzel–Fox Integral Operators

Cited by 8 publications

References 11 publications

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

On the Topology $\tau_{R}^{\diamond}$ of Primal Topological Spaces

Some Generalized Properties of Poly-Daehee Numbers and Polynomials Based on Apostol–Genocchi Polynomials

Computation of certain integral formulas involving generalized Wright function

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