Some Approximation Properties of New Kind of Baskakov–Schurer–Szász Operators

Md Nasiruzzaman; Mohammad Mursaleen; Naim L. Braha; Toufik Mansour

doi:10.1007/s40010-026-01044-y

Some Approximation Properties of New Kind of Baskakov–Schurer–Szász Operators

Md Nasiruzzaman
, Mohammad Mursaleen
, Naim L. Braha
, Toufik Mansour

Department of Mathematics

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

Abstract

This paper introduces a new class of parametric Baskakov–Schurer–Szász operators based on sequences of continuous functions on. These operators extend the classical Baskakov–Schurer–Szász framework by incorporating a novel parameter and function sequence. We establish a Korovkin-type theorem, prove a Grüss–Voronovskaya-type result, and determine the rate of convergence. Additionally, we analyze these generalizations within weighted spaces. The final section is dedicated to proving shape-preserving properties, demonstrating that our results encompass the classical operators as a special case.

Original language	English
Journal	Proceedings of the National Academy of Sciences India Section A - Physical Sciences
DOIs	https://doi.org/10.1007/s40010-026-01044-y
State	Accepted/In press - 2026

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to The National Academy of Sciences, India 2026.

Keywords

Baskakov–Schurer–Szász operators
Grüss–Voronovskaya
Korovkin type theorem
Shape preserving properties
Voronovskaya type theorem
rate of convergence

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1007/s40010-026-01044-y

Cite this

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title = "Some Approximation Properties of New Kind of Baskakov–Schurer–Sz{\'a}sz Operators",

abstract = "This paper introduces a new class of parametric Baskakov–Schurer–Sz{\'a}sz operators based on sequences of continuous functions on. These operators extend the classical Baskakov–Schurer–Sz{\'a}sz framework by incorporating a novel parameter and function sequence. We establish a Korovkin-type theorem, prove a Gr{\"u}ss–Voronovskaya-type result, and determine the rate of convergence. Additionally, we analyze these generalizations within weighted spaces. The final section is dedicated to proving shape-preserving properties, demonstrating that our results encompass the classical operators as a special case.",

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journal = "Proceedings of the National Academy of Sciences India Section A - Physical Sciences",

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AU - Nasiruzzaman, Md

AU - Mursaleen, Mohammad

AU - Braha, Naim L.

AU - Mansour, Toufik

N1 - Publisher Copyright: © The Author(s), under exclusive licence to The National Academy of Sciences, India 2026.

PY - 2026

Y1 - 2026

N2 - This paper introduces a new class of parametric Baskakov–Schurer–Szász operators based on sequences of continuous functions on. These operators extend the classical Baskakov–Schurer–Szász framework by incorporating a novel parameter and function sequence. We establish a Korovkin-type theorem, prove a Grüss–Voronovskaya-type result, and determine the rate of convergence. Additionally, we analyze these generalizations within weighted spaces. The final section is dedicated to proving shape-preserving properties, demonstrating that our results encompass the classical operators as a special case.

AB - This paper introduces a new class of parametric Baskakov–Schurer–Szász operators based on sequences of continuous functions on. These operators extend the classical Baskakov–Schurer–Szász framework by incorporating a novel parameter and function sequence. We establish a Korovkin-type theorem, prove a Grüss–Voronovskaya-type result, and determine the rate of convergence. Additionally, we analyze these generalizations within weighted spaces. The final section is dedicated to proving shape-preserving properties, demonstrating that our results encompass the classical operators as a special case.

KW - Baskakov–Schurer–Szász operators

KW - Grüss–Voronovskaya

KW - Korovkin type theorem

KW - Shape preserving properties

KW - Voronovskaya type theorem

KW - rate of convergence

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DO - 10.1007/s40010-026-01044-y

M3 - Article

AN - SCOPUS:105039687978

SN - 0369-8203

JO - Proceedings of the National Academy of Sciences India Section A - Physical Sciences

JF - Proceedings of the National Academy of Sciences India Section A - Physical Sciences

ER -

Some Approximation Properties of New Kind of Baskakov–Schurer–Szász Operators

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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