On a New Modification of Baskakov Operators with Higher Order of Approximation

Abstract

A new Goodman–Sharma-type modification of the Baskakov operator is presented for approximation of bounded and continuous functions on [0,∞). We study the approximation error of the proposed operator. Our main results are a direct theorem and strong converse theorem with respect to a related K-functional. Both theorems give complete characterization of the uniform approximation error in means of the K-functional. The new operator suggested by the authors is linear but non-positive. However, it has the advantage of a higher order of approximation compared to the Goodman–Sharma variant of the Baskakov operator defined in 2005 by Finta. The results of computational simulations are given.

Keywords

• Baskakov–Durrmeyer operator
• Goodman–Sharma operator
• non-positive operator
• direct theorem
• strong converse theorem
• K-functional