Bögel Functions, Tensor Products and Blending Approximation

Badea, Cătălin; Cottin, Claudia; Gonska, Heiner

doi:10.1002/mana.19951730103

Cited by 4 publications

(3 citation statements)

References 28 publications

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“…As a general source for related material we mention here the book by F. Altomare and M. Campiti [1]. Recent contributions influenced by the Romanian school are due to D. Andrica, C. Badea, I. Raşa, and several of their collaborators (see, e.g., [2], [3], [4], [47]). As articles from China papers by Tian-ping Chen and Wen-ge Zhu ([63], [8]) have to be mentioned.…”

Section: Discussionmentioning

confidence: 99%

The rate of convergence of bounded linear processes on spaces of continuous functions

Gonska

2023

J. Numer. Anal. Approx. Theory

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Quantitative Korovkin-type theorems for approximation by bounded linear operators defined on \(C(X,d)\) are given, where \((X,d)\) is a compact metric space. Special emphasis is on positive linear operators.As is known from previous work of Newman and Shapiro, Jimenez Pozo, Nishishiraho and the author, among others, there are two possible ways to obtain error estimates for bounded linear operator approximation: the so-called direct approach, and the smoothing technique.We give various generalizations and refinements of earlier results which were obtained by using both techniques. Furthermore, it will be shown that, in a certain sense, none of the two methods is superior to the other one.

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Section: Discussionmentioning

confidence: 99%

The rate of convergence of bounded linear processes on spaces of continuous functions

Gonska

2023

J. Numer. Anal. Approx. Theory

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“…In order to make analysis in multidimensional spaces, Karl B ögel introduced the concepts of B-continuous and B-differentiable function in [16,17]. In [31], the authors discussed some significance role of the B ögel space. They proved that the space of all bounded B ögel functions is isometrically isometric with the completion of the blending function space with respect to suitable norm.…”

Section: Some Basic Definitions For Associated Gbs (Generalized Boole...mentioning

confidence: 99%

Approximation by associated GBS operators of Szász-Mirakjan type operators

Yadav

Meher

Mishra

2021

Filomat

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In this article, the approximation properties of bivariate Sz?sz-Mirakjan type operators are studied for the function of two variables and rate of convergence of the bivariate operators is determined in terms of total and partial modulus of continuity. An associated GBS (Generalized Boolean Sum)-form of the bivariate Sz?sz-Mirakjan type operators is considered for the function of two variables to find an approximation of B-continuous and B-differentiable function in the B?gel?s space. Further, the degree of approximation of the GBS type operators is found in terms of mixed modulus of smoothness and functions belonging to the Lipschitz class as well as a pioneering result is obtained in terms of Peetre K-functional. Finally, the rate of convergence of the bivariate Sz?sz-Mirakjan type operators and the associated GBS type operators are examined through graphical representation for the finite and infinite sum which shows that the rate of convergence of the associated GBS type operators is better than the bivariate Sz?sz-Mirakjan type operators and also a comparison is taken place for the bivariate operators with bivariate Kantorovich operators.

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“…In order to make analysis in multidimensional spaces, Karl Bögel introduced the concepts of B-continuous and B-differentiable function in [6,7]. In [11], the authors discussed some significance role of the Bögel space. They proved that the space of all bounded Bögel functions is isometrically isometric with the completion of the blending function space with respect to suitable norm.…”

Section: Basic Properties Of the Bivariate Operatorsmentioning

confidence: 99%

Approximation of associated GBS operators by Szasz-Mirakjan type operators

Yadav¹,

Meher²,

Mishra³

2020

Preprint

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In this article, the approximation properties of the Szász-Mirakjan type operators are studied for the function of two variables and the rate of convergence of the bivariate operators is determined in terms of total and partial modulus of continuity. An associated GBS (Generalized Boolean Sum)-form of the bivariate Szász-Mirakjan type operators is considered for the function of two variables to find an approximation of B-continuous and B-differentiable function in the Bögel's space. Further, the degree of approximation of the GBS type operators is found in terms of mixed modulus of smoothness and functions belonging to the Lipschitz class as well as a pioneering result is obtained in terms of Peetre K-functional. Finally, the rate of convergence of the bivariate Szász-Mirakjan type operators and the associated GBS type operators are examined through graphical representation for the finite and infinite sum which shows that the rate of convergence of the associated GBS type operators is better than the bivariate Szász-Mirakjan type operators.

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Bögel Functions, Tensor Products and Blending Approximation

Cited by 4 publications

References 28 publications

The rate of convergence of bounded linear processes on spaces of continuous functions

The rate of convergence of bounded linear processes on spaces of continuous functions

Approximation by associated GBS operators of Szász-Mirakjan type operators

Approximation of associated GBS operators by Szasz-Mirakjan type operators

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