Korean J. Math.  Vol 27, No 2 (2019)  pp.505-514
DOI: https://doi.org/10.11568/kjm.2019.27.2.505

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

M. Mursaleen, Faisal Khan, Mohd Saif, Abdul Hakim Khan

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 $\{z:\left\vert z\right\vert \leq \rho \},$ ${ \rho >0}$.


Keywords


$(p,q)$-integers; $% (p,q)$-Bernstein operators; divided difference; analytic function; uniform convergence.

Subject classification

41A65, 47A58, 30H05

Sponsor(s)



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