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Keywords = Pólya–Eggenberger distribution

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14 pages, 303 KiB  
Article
Bézier-Summation-Integral-Type Operators That Include Pólya–Eggenberger Distribution
by Syed Abdul Mohiuddine, Arun Kajla and Abdullah Alotaibi
Mathematics 2022, 10(13), 2222; https://doi.org/10.3390/math10132222 - 25 Jun 2022
Cited by 10 | Viewed by 1766
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 [...] Read more.
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. Full article
13 pages, 274 KiB  
Article
Stancu Type Baskakov—Durrmeyer Operators and Approximation Properties
by Adem Kilicman, Mohammad Ayman Mursaleen and Ahmed Ahmed Hussin Ali Al-Abied
Mathematics 2020, 8(7), 1164; https://doi.org/10.3390/math8071164 - 15 Jul 2020
Cited by 30 | Viewed by 2802
Abstract
In this article, we introduce Stancu type generalization of Baskakov–Durrmeyer operators by using inverse Pólya–Eggenberger distribution. We discuss some basic results and approximation properties. Moreover, we study the statistical convergence for these operators. Full article
(This article belongs to the Special Issue Approximation Theory and Methods 2020)
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