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

Author

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

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.

Suggested Citation

  • Wen-Tao Cheng & Md Nasiruzzaman & Syed Abdul Mohiuddine, 2022. "Stancu-Type Generalized q -Bernstein–Kantorovich Operators Involving Bézier Bases," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2057-:d:838556
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