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Keywords = Jakimovski–Leviatan operators

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11 pages, 289 KB  
Article
Unveiling the Potential of Sheffer Polynomials: Exploring Approximation Features with Jakimovski–Leviatan Operators
by Mohra Zayed, Shahid Ahmad Wani and Mohammad Younus Bhat
Mathematics 2023, 11(16), 3604; https://doi.org/10.3390/math11163604 - 21 Aug 2023
Cited by 3 | Viewed by 1151
Abstract
In this article, we explore the construction of Jakimovski–Leviatan operators for Durrmeyer-type approximation using Sheffer polynomials. Constructing positive linear operators for Sheffer polynomials enables us to analyze their approximation properties, including weighted approximations and convergence rates. The application of approximation theory has earned [...] Read more.
In this article, we explore the construction of Jakimovski–Leviatan operators for Durrmeyer-type approximation using Sheffer polynomials. Constructing positive linear operators for Sheffer polynomials enables us to analyze their approximation properties, including weighted approximations and convergence rates. The application of approximation theory has earned significant attention from scholars globally, particularly in the fields of engineering and mathematics. The investigation of these approximation properties and their characteristics holds considerable importance in these disciplines. Full article
21 pages, 330 KB  
Article
On the Approximation by Bivariate Szász–Jakimovski–Leviatan-Type Operators of Unbounded Sequences of Positive Numbers
by Abdullah Alotaibi
Mathematics 2023, 11(4), 1009; https://doi.org/10.3390/math11041009 - 16 Feb 2023
Cited by 10 | Viewed by 1656
Abstract
In this paper, we construct the bivariate Szász–Jakimovski–Leviatan-type operators in Dunkl form using the unbounded sequences αnβm and ξm of positive numbers. Then, we obtain the rate of convergence in terms of the weighted modulus of continuity of [...] Read more.
In this paper, we construct the bivariate Szász–Jakimovski–Leviatan-type operators in Dunkl form using the unbounded sequences αnβm and ξm of positive numbers. Then, we obtain the rate of convergence in terms of the weighted modulus of continuity of two variables and weighted approximation theorems for our operators. Moreover, we provide the degree of convergence with the help of bivariate Lipschitz-maximal functions and obtain the direct theorem. Full article
21 pages, 330 KB  
Article
Approximation of GBS Type q-Jakimovski-Leviatan-Beta Integral Operators in Bögel Space
by Abdullah Alotaibi
Mathematics 2022, 10(5), 675; https://doi.org/10.3390/math10050675 - 22 Feb 2022
Cited by 13 | Viewed by 2149
Abstract
In the present article, we introduce the bivariate variant of Beta integral type operators based on Appell polynomials via q-calculus. We study the local and global type approximation properties for these new operators. Next, we introduce the GBS form for these new [...] Read more.
In the present article, we introduce the bivariate variant of Beta integral type operators based on Appell polynomials via q-calculus. We study the local and global type approximation properties for these new operators. Next, we introduce the GBS form for these new operators and then study the degree of approximation by means of modulus of smoothness, mixed modulus of smoothness and Lipschitz class of Bögel continuous functions. Full article
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