On Generalized Picard Integral Operators

Ali Aral ()
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Ali Aral: Kirikkale University, Faculty of Science and Arts, Department of Mathematics

A chapter in Advances in Summability and Approximation Theory, 2018, pp 157-168 from Springer

Abstract: Abstract In the paper, we constructed a class of linear positive operators generalizing Picard integral operators which preserve the functions $$e^{\mu x}$$ and $$e^{2\mu x},$$ $$\mu >0.$$ We show that these operators are approximation processes in a suitable weighted spaces. The uniform weighted approximation order of constructed operators is given via exponential weighted modulus of smoothness. We also obtain their shape preserving properties considering exponential convexity.

Keywords: Voronovskaya-type theorems; Weighted modulus of continuity; Primary 41A36; Secondary 41A25 (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-3077-3_9

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DOI: 10.1007/978-981-13-3077-3_9

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