Statistical approximation by (p; q)-analogue of Bernstein-Stancu Operators

Asif Khan, Vinita Sharma

Abstract


In this paper, some approximation properties of (p; q)-analogue of Bernstein-Stancu Operators has been studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated. Monotonicity of (p; q)-Bernstein-Stancu Operators and a global approximation theorem by means of Ditzian-Totik modulus of smoothness is established.
A quantitative Voronovskaja type theorem is developed for these operators. Furthermore, we show comparisons and some illustrative graphics for the convergence of operators to a function.


Keywords


(p; q)-integers; (p; q)-Bernstein-Stancu operators; Positive linear operators; Korovkin type approximation; Statistical convergence; Monotonicity for convex functions; Ditzian-Totik modulus of smoothness; Voronovskaja type theorem.

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