Higher order approximation of functions by modified Goodman-Sharma operators

Authors : Rumen Uluchev, Ivan Gadjev, Parvan Parvanov

Pages : 180-195

Doi:10.33205/cma.1563047

View : 99 | Download : 45

Publication Date : 2024-12-15

Article Type : Research Paper

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