On the Approximation by Bivariate Szász–Jakimovski–Leviatan-Type Operators of Unbounded Sequences of Positive Numbers

Alotaibi, Abdullah

doi:10.3390/math11041009

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…Recently, they have remarkable studies in operator theory [6][7][8][9], analytic function theory [10], and other fields [11,12]. Now, we define the Durrmeyer-type generalization of Szász operators involving confluent Appell polynomials…”

Section: Introductionmentioning

confidence: 99%

Szász–Durrmeyer Operators Involving Confluent Appell Polynomials

Kanat,

Erdal

2024

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This article is concerned with the Durrmeyer-type generalization of Szász operators, including confluent Appell polynomials and their approximation properties. Also, the rate of convergence of the confluent Durrmeyer operators is found by using the modulus of continuity and Peetre’s K-functional. Then, we show that, under special choices of A(t), the newly constructed operators reduce confluent Hermite polynomials and confluent Bernoulli polynomials, respectively. Finally, we present a comparison of newly constructed operators with the Durrmeyer-type Szász operators graphically.

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Section: Introductionmentioning

confidence: 99%

Szász–Durrmeyer Operators Involving Confluent Appell Polynomials

Kanat,

Erdal

2024

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Approximation Properties of Extended Beta-Type Szász–Mirakjan Operators

Rao,

Raiz,

Ayman-Mursaleen

et al. 2023

Iran J Sci

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In this article, we introduce generalized beta extension of Sz$$\acute{a}$$ a ´ sz-integral type operators and study their approximation properties. First, we calculate the some estimates for these operators. Further, we study the uniform convergence and order of approximation in terms of Korovkin-type theorem and modulus of continuity for the space of univariate continuous functions and bivariate continuous functions in their sections.. Moreover, numerical estimates and graphical representations for convergence of one- and two-dimensional sequences of operators are studied. In continuation, local and global approximation properties are studied in terms of the first- and second-order modulus of smoothness, Peetre’s K-functional and weight functions in various functional spaces.

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Approximation results for beta Jakimovski-Leviatan type operators via q-analogue

Nasiruzzaman,

Tom,

Serra-Capizzano

et al. 2023

Filomat

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We construct a new version of q-Jakimovski-Leviatan type integral operators and show that set of all continuous functions f defined on [0,?) are uniformly approximated by our new operators. Finally we construct the Stancu type operators and obtain approximation properties in weighted spaces. Moreover, with the aid of modulus of continuity we discuss the rate of convergence, Lipschitz type maximal approximation and some direct theorems.

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On the Approximation by Bivariate Szász–Jakimovski–Leviatan-Type Operators of Unbounded Sequences of Positive Numbers

Cited by 3 publications

References 28 publications

Szász–Durrmeyer Operators Involving Confluent Appell Polynomials

Szász–Durrmeyer Operators Involving Confluent Appell Polynomials

Approximation Properties of Extended Beta-Type Szász–Mirakjan Operators

Approximation results for beta Jakimovski-Leviatan type operators via q-analogue

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