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

TL;DR

This paper introduces a new modification of Baskakov operators that achieves higher order approximation for bounded continuous functions on [0, ∞), with proven error bounds and theorems, despite being non-positive.

Contribution

It presents a novel Goodman-Sharma type Baskakov operator with improved approximation order and establishes theoretical error bounds and convergence theorems.

Findings

The new operator has higher approximation order than previous variants.

The paper proves direct and strong converse theorems for the operator.

The operator is linear but not positive, yet effective for approximation.

Abstract

A new Goodman-Sharma modification of the Baskakov operator is presented for approximation of bounded and continuous on $[0,\,\infty)$ functions. In our study on the approximation error of the proposed operator we prove direct and strong converse theorems with respect to a related K-functional. This operator is linear but not 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.