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

University of Haifa

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

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

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10.1007/s40010-026-01044-y

Cite this

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

abstract = "This paper introduces a new class of parametric Baskakov{\textendash}Schurer{\textendash}Sz{\'a}sz operators based on sequences of continuous functions on. These operators extend the classical Baskakov{\textendash}Schurer{\textendash}Sz{\'a}sz framework by incorporating a novel parameter and function sequence. We establish a Korovkin-type theorem, prove a Gr{\"u}ss{\textendash}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.",

keywords = "Baskakov{\textendash}Schurer{\textendash}Sz{\'a}sz operators, Gr{\"u}ss{\textendash}Voronovskaya, Korovkin type theorem, Shape preserving properties, Voronovskaya type theorem, rate of convergence",

author = "Md Nasiruzzaman and Mohammad Mursaleen and Braha, \{Naim L.\} and Toufik Mansour",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to The National Academy of Sciences, India 2026.",

year = "2026",

doi = "10.1007/s40010-026-01044-y",

language = "English",

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TY - JOUR

T1 - Some Approximation Properties of New Kind of Baskakov–Schurer–Szász Operators

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

UR - https://www.scopus.com/pages/publications/105039687978

U2 - 10.1007/s40010-026-01044-y

DO - 10.1007/s40010-026-01044-y

M3 - Article

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

Keywords

ASJC Scopus subject areas

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