Higher order approximation of functions by modified Goodman-Sharma operators

Year 2024, Volume: 7 Issue: 4, 180 - 195, 15.12.2024

Rumen Uluchev , Ivan Gadjev , Parvan Parvanov

https://doi.org/10.33205/cma.1563047

Abstract

Here we study the approximation properties of a modified Goodman-Sharma operator recently considered by Acu and Agrawal in [1]. This operator is linear but not positive. It has the advantage of a higher order of approximation of functions compared with the Goodman-Sharma operator. We prove direct and strong converse theorems in terms of a related K-functional.

Keywords

Bernstein-Durrmeyer operator, Goodman-Sharma operator, Direct theorem, Strong converse theorem, K-functional

Project Number

BG-RRP-2.004-0008

Thanks

This study is financed by the European Union-NextGenerationEU, through the National Recovery and Resilience Plan of the Republic of Bulgaria, project No. BG-RRP-2.004-0008.

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