Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON ESTIMATION OF UNIFORM CONVERGENCE OF ANALYTIC FUNCTIONS BY (p, q)-BERNSTEIN OPERATORS

  • Mursaleen, M. (Department of Mathematics Aligarh Muslim University) ;
  • Khan, Faisal (Department of Mathematics Aligarh Muslim University) ;
  • Saif, Mohd (Department of Mathematics Aligarh Muslim University) ;
  • Khan, Abdul Hakim (Department of Mathematics Aligarh Muslim University)
  • Received : 2019.02.17
  • Accepted : 2019.06.07
  • Published : 2019.06.30
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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 $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, then $B^n_{p,q}(g;z){\rightarrow}g(z)(n{\rightarrow}{\infty})$ uniformly on any compact set in the given disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, ${\rho}>0$.

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References

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