Modified Stancu operators based on inverse Polya Eggenberger distribution

Abstract In this paper, we construct a sequence of modified Stancu-Baskakov operators for a real valued function bounded on [ 0, ∞ ) $[0,\infty)$, based on a function τ ( x ) $\tau(x)$. This function τ ( x ) $\tau(x)$ is infinite times continuously differentiable on [ 0, ∞ ) $[0,\infty)$ and satisfy the conditions τ ( 0 ) = 0, τ ′ ( x ) > 0 $\tau (0)=0,~\tau ^{\prime}(x)>0$ and τ ″ ( x ) $\tau^{\prime\prime}(x)$ is bounded for all x ∈ [ 0, ∞ ) $x\in {}[0,\infty)$. We study the degree of approximation of these operators by means of the Peetre K-functional and the Ditzian-Totik modulus of smoothness. The quantitative Voronovskaja-type theorems are also established in terms of the first order Ditzian-Totik modulus of smoothness.

Abstract licence: CC BY-NC-ND

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