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On estimation of uniform convergence of analytic functions by $(p,q)$-Bernstein operators

Abdul Hakim Khan|M. Mursaleen|Faisal Khan|Mohd Saif
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2019.06|한국수학논문집 (Korean Journal of Mathematics)|제27권 제2호|pp. 505-514

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참고문헌

키워드

divided difference$(panalytic functionq)$-integers$% (pq)$-Bernstein operatorsuniform convergence.
주제분류수학

초록

In this paper we study the approximation properties of a continuous function by the sequence of $(p,q)$-Bernstein operators for $q>p>1$. We obtain bounds of {$(p,q)$-}Bernstein operators. Further we prove that if a continuous function admits an analytic continuation into the disk $\{z:\left\vert z\right\vert \leq \rho \}$, then $ B_{p,q}^{n}(g;z)\rightarrow g(z)$ ($n\rightarrow \infty $) uniformly on any compact set in the given disk $\{z:\left\vert z\right\vert \leq \rho \},$ ${ \rho >0}$.

Abstract

In this paper we study the approximation properties of a continuous function by the sequence of $(p,q)$-Bernstein operators for $q>p>1$. We obtain bounds of {$(p,q)$-}Bernstein operators. Further we prove that if a continuous function admits an analytic continuation into the disk $\{z:\left\vert z\right\vert \leq \rho \}$, then $ B_{p,q}^{n}(g;z)\rightarrow g(z)$ ($n\rightarrow \infty $) uniformly on any compact set in the given disk $\{z:\left\vert z\right\vert \leq \rho \},$ ${ \rho >0}$.

참고문헌 (23)

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