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Direct Results for Certain Summation-Integral Type Baskakov–Szász Operators

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Abstract

In the present article we define a mixed hybrid operator based on two parameters. As special case, we get the genuine hybrid operators viz. Phillips and Baskakov–Szász type operators. We estimate moments and obtain some direct results, which include the Voronovskaja type asymptotic formula, local approximation, error estimation in terms of the modulus of continuity and weighted approximation. Furthermore, we obtain the rate of convergence for unbounded functions with derivatives of bounded variation by these operators. The paper contains also numerical examples based on Maple algorithms, which verify approximation properties of these operators.

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Correspondence to Ana Maria Acu.

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Acu, A.M., Gupta, V. Direct Results for Certain Summation-Integral Type Baskakov–Szász Operators. Results Math 72, 1161–1180 (2017). https://doi.org/10.1007/s00025-016-0603-2

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