On estimation of uniform convergence of analytic functions by $(p,q)$-Bernstein operators
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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 $\{z:\left\vert z\right\vert \leq \rho \},$ ${ \rho >0}$.
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