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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 $\{z:\left\vert z\right\vert \leq \rho \},$ ${ \rho >0}$.
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참고문헌 (23)
참고문헌 신청
T. Acar / 2016 / (p; q)-generalization of Sza sz-Mirakyan operators / Math. Methods Appl. Sci 9(10):2685~2695
T. Acar / 2016 / Approximation by bivariate (p; q)-Bernstein Kantorovich operators / Iranian Jour. Sci. Techn., Trans A: Science 42(2):655~662
T. Acar / 2016 / On Kantorovich modication of (p; q)-Baskakov operators / J. Inequal. Appl :98
S. N. Bernstein / 1912 / Demonstration du theoreme de Weierstrass fondee sur la calcul des probabilites / Commun. Soc. Math. Charkow Ser 13:1~2
H. Bin Jebreen / 2018 / Approximation by quaternion (p; q)-Bernstein polynomials and Voronovskaja type result on compact disk / Adv. Difference Equ 2018:448
T. Acar / 2016 / Approximation by bivariate (p; q)-Bernstein Kantorovich operators / Iranian Jour. Sci. Techn., Trans A: Science 42(2):655~662
T. Acar / 2016 / On Kantorovich modication of (p; q)-Baskakov operators / J. Inequal. Appl :98
S. N. Bernstein / 1912 / Demonstration du theoreme de Weierstrass fondee sur la calcul des probabilites / Commun. Soc. Math. Charkow Ser 13:1~2
H. Bin Jebreen / 2018 / Approximation by quaternion (p; q)-Bernstein polynomials and Voronovskaja type result on compact disk / Adv. Difference Equ 2018:448
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