Weighted gamma-K-functional and gamma-Modulus of Smoothness on the Semiaxis

Abstract

In this paper we investigate the gamma-relative differentiation by the motivation of amending the order of the weighted polynomial approximation on the semiaxis for certain functions. With the help of this we give some definitions of generalized Sobolev spaces, K-functionals and moduli of smoothness. We prove theorems for estimating these things with each other, in the case of first order we prove equivalence. We remark some possible applications and other generalizations too.