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

Syed Abdul Mohiuddine, Arun Kajla and Abdullah Alotaibi
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Syed Abdul Mohiuddine: Department of General Required Courses, Mathematics, Faculty of Applied Studies, 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

Mathematics, 2022, vol. 10, issue 13, 1-14

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.

Keywords: Stancu operators; Pólya–Eggenberger distribution; Bézier curves; rate of convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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