Higher order approximation of functions by modified Goodman-Sharma operators

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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