On the order of approximation by modified summation-integral-type operators based on two parameters

• Autorzy: Mohiuddine Syed Abdul , Singh Karunesh Kumar , Alotaibi Abdullah

Identyfikatory

DOI

10.1515/dema-2022-0182

• Języki publikacji: EN

Abstrakty

EN

In this article, we the study generalized family of positive linear operators based on two parameters, which are a broad family of many well-known linear positive operators, e.g., Baskakov-Durrmeyer, Baskakov-Szász, Szász-Beta,Lupaş-Beta, Lupaş-Szász, genuine Bernstein-Durrmeyer, and Pǎltǎnea. We first find direct estimates in terms of the second-order modulus of continuity, then we find an estimate of error in the Ditzian-Totik modulus of smoothness. Then we discuss the rate of approximation for functions in the Lipschitz class. Furthermore, we study the pointwise Grüss-Voronovskaja-type result and also establish the Grüss-Voronovskaja-type asymptotic formula in quantitative form.

Słowa kluczowe

EN

Ditzian-Totik modulus of smoothness; Peetre's K-functional; Grüss-Voronovskaja-type asymptotic formula

PL

moduł gładkości Ditziana-Totika; twierdzenie Peetre'a; formuła asymptotyczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220182
• Opis fizyczny: Bibliogr. 43 poz., tab.

Twórcy

autor

Mohiuddine Syed Abdul

• Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
• Department of General Required Courses, Mathematics, The Applied College, King Abdulaziz University, Jeddah 21589, Saudi Arabia

autor

Singh Karunesh Kumar

• Department of Applied Sciences and Humanities, Institute of Engineering and Technology, Dr. A. P. J. Abdul Kalam Technical University, Sitapur Road, Lucknow 226021, Uttar Pradesh, India

autor

Alotaibi Abdullah

• Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).