An application of Bernstein-Durrmeyer operators

Abstract

In the present paper, we find that the Bernstein-Durrmeyer operators, besides their better applications in approximation theory and some other fields, are good tools in constructing translation network. With the help of the de la Vallée properties of the Bernstein-Durrmeyer operators a sequence of translation network operators is constructed and its degree of approximation is dealt.

Applications of Bernstein-Durrmeyer operators in estimating the covering number

“…Theory Appl., Vol. 26, No.2 (2010) 187 translation networks(see [9]), and in estimating the l 2 −norm of Mercer kernel matrices(see [10]). …”

Applications of the Bernstein-Durrmeyer operators in estimating the norm of Mercer kernel matrices

“…[16][17][18][19][20][21][22][23]),in estimating the regularization error of learning theory(see [24]), and,as a better tool, in constructing neural and translation networks(see [25][26]), can be used to estimate the Rayleigh entropy number of the Mercer kernel…”