Open Access

ARTICLE

Note on a New Construction of Kantorovich Form q-Bernstein Operators Related to Shape Parameter λ

Qingbo Cai¹, Reşat Aslan^2,*
1 Fujian Provincial Key Laboratory of Data-Intensive Computing, Key Laboratory of Intelligent Computing and Information Processing, School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, 362000, China
2 Department of Mathematics, Faculty of Sciences and Arts, Harran University, Şanlıurfa, 63300, Turkey
* Corresponding Author: Reşat Aslan. Email:
(This article belongs to this Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2022, 130(3), 1479-1493. https://doi.org/10.32604/cmes.2022.018338

Received 16 July 2021; Accepted 23 September 2021; Issue published 30 December 2021

Abstract

The main purpose of this paper is to introduce some approximation properties of a Kantorovich kind q-Bernstein operators related to Bézier basis functions with shape parameter . Firstly, we compute some basic results such as moments and central moments, and derive the Korovkin type approximation theorem for these operators. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz-type class and Peetre’s K-functional, respectively. Lastly, with the aid of Maple software, we present the comparison of the convergence of these newly defined operators to the certain function with some graphical illustrations and error estimation table.

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Keywords

q-calculus; λ-Bernstein polynomials; order of convergence; Lipschitz-type function; Peetre’s K-functional

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Citations