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Bézier-Summation-Integral-Type Operators That Include Pólya–Eggenberger Distribution

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  • 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)

  • Arun Kajla

    (Department of Mathematics, Central University of Haryana, Mahendragarh 123029, Haryana, India)

  • Abdullah Alotaibi

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

Abstract

We define the summation-integral-type operators involving the ideas of Pólya–Eggenberger distribution and Bézier basis functions, and study some of their basic approximation properties. In addition, by means of the Ditzian–Totik modulus of smoothness, we study a direct theorem as well as a quantitative Voronovskaja-type theorem for our newly constructed operators. Moreover, we investigate the approximation of functions with derivatives of bounded variation (DBV) of the aforesaid operators.

Suggested Citation

  • Syed Abdul Mohiuddine & Arun Kajla & Abdullah Alotaibi, 2022. "Bézier-Summation-Integral-Type Operators That Include Pólya–Eggenberger Distribution," Mathematics, MDPI, vol. 10(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2222-:d:847507
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    References listed on IDEAS

    as
    1. Deo, Naokant & Dhamija, Minakshi & Miclăuş, Dan, 2016. "Stancu–Kantorovich operators based on inverse Pólya–Eggenberger distribution," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 281-289.
    2. Abel, Ulrich & Ivan, Mircea & Păltănea, Radu, 2015. "The Durrmeyer variant of an operator defined by D.D. Stancu," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 116-123.
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