APPROXIMATION BY DURRMEYER TYPE NEURAL NETWORK OPERATORS

Abstract

In approximation theory, various type Durrmeyer operators have been defined and their approximation properties have been investigated. We include some of them in the article. In this article, wedefine aDurrmeyer type Neural Network operators within a compact interval [a,b] as follows, b ⌊nb⌋ k=⌈na⌉ ND n(f;x) = ˆ H(nx −k)1 I a f (t) ˆ H(nt −k)dt ⌊nb⌋ k=⌈na⌉ ˆ H(nx −k) . Moreover we examine approximation properties of this operators in some function spaces.