Stancu-Type Generalized q -Bernstein–Kantorovich Operators Involving Bézier Bases

Wen-Tao Cheng, Md Nasiruzzaman and Syed Abdul Mohiuddine
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Wen-Tao Cheng: School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China
Md Nasiruzzaman: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Syed Abdul Mohiuddine: Department of General Required Courses, Mathematics, Faculty of Applied Studies, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 12, 1-14

Abstract: We construct the Stancu-type generalization of q -Bernstein operators involving the idea of Bézier bases depending on the shape parameter − 1 ≤ ζ ≤ 1 and obtain auxiliary lemmas. We discuss the local approximation results in term of a Lipschitz-type function based on two parameters and a Lipschitz-type maximal function, as well as other related results for our newly constructed operators. Moreover, we determine the rate of convergence of our operators by means of Peetre’s K -functional and corresponding modulus of continuity.

Keywords: (?, q )-Bernstein operators; Bézier bases; uniform convergence; Lipschitz-type functions; rate of convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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