On approximation properties of some non-positive Bernstein-Durrmeyer type operators

Abstract

In this paper we shall introduce a new type of Bernstein Durrmeyer operators which are not positive on the entire interval [0, 1]. For these operators we will study the uniform convergence on all continuous functions on [0, 1] as well as a result given in terms of modulus of continuity ω(f, δ). A Voronovskaja type theorem will be proved as well.

Keywords

• linear operators
• non-positive operators
• approximation by operators
• quantitative results
• bernstein-durrmeyer type operators
• primary 47a58, 41a25
• secondary 47a30, 41a10