Approximation properties by Bézier variant of the Baskakov–Schurer–Szász–Stancu operators

Naim Latif Braha; Toufik Mansour; Mohammad Mursaleen

doi:10.1002/mma.9755

Approximation properties by Bézier variant of the Baskakov–Schurer–Szász–Stancu operators

Naim Latif Braha, Toufik Mansour, Mohammad Mursaleen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we have construct a new version of the Bézier-type Baskakov–Schurer–Szász–Stancu operators. For this new class of operators, uniform convergence is shown in any compact subset or positive real line. We prove Korovkin-type theorem, Voronovskaya-type theorem, and Grüss–Voronovskaya-type theorem. Moreover, at the end, we express the behavior of the operators in the Lipschitz-type space using the modulus of continuity and smoothness.

Original language	English
Pages (from-to)	2419-2433
Number of pages	15
Journal	Mathematical Methods in the Applied Sciences
Volume	47
Issue number	4
DOIs	https://doi.org/10.1002/mma.9755
State	Published - 15 Mar 2024

Bibliographical note

Publisher Copyright:
© 2023 John Wiley & Sons Ltd.

Keywords

Bézier form of the Baskakov–Schurer–Szász–Stancu operators
Grüss–Voronovskaya-type theorem
Korovkin-type theorem
Voronovskaya-type theorem

ASJC Scopus subject areas

General Mathematics
General Engineering

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10.1002/mma.9755

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title = "Approximation properties by B{\'e}zier variant of the Baskakov–Schurer–Sz{\'a}sz–Stancu operators",

abstract = "In this paper, we have construct a new version of the B{\'e}zier-type Baskakov–Schurer–Sz{\'a}sz–Stancu operators. For this new class of operators, uniform convergence is shown in any compact subset or positive real line. We prove Korovkin-type theorem, Voronovskaya-type theorem, and Gr{\"u}ss–Voronovskaya-type theorem. Moreover, at the end, we express the behavior of the operators in the Lipschitz-type space using the modulus of continuity and smoothness.",

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AU - Mansour, Toufik

AU - Mursaleen, Mohammad

PY - 2024/3/15

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N2 - In this paper, we have construct a new version of the Bézier-type Baskakov–Schurer–Szász–Stancu operators. For this new class of operators, uniform convergence is shown in any compact subset or positive real line. We prove Korovkin-type theorem, Voronovskaya-type theorem, and Grüss–Voronovskaya-type theorem. Moreover, at the end, we express the behavior of the operators in the Lipschitz-type space using the modulus of continuity and smoothness.

AB - In this paper, we have construct a new version of the Bézier-type Baskakov–Schurer–Szász–Stancu operators. For this new class of operators, uniform convergence is shown in any compact subset or positive real line. We prove Korovkin-type theorem, Voronovskaya-type theorem, and Grüss–Voronovskaya-type theorem. Moreover, at the end, we express the behavior of the operators in the Lipschitz-type space using the modulus of continuity and smoothness.

KW - Bézier form of the Baskakov–Schurer–Szász–Stancu operators

KW - Grüss–Voronovskaya-type theorem

KW - Korovkin-type theorem

KW - Voronovskaya-type theorem

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JO - Mathematical Methods in the Applied Sciences

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ER -

Approximation properties by Bézier variant of the Baskakov–Schurer–Szász–Stancu operators

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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