Equivalence of <i>K</i>-functionals and modulus of smoothness constructed by generalized Jacobi transform

Abstract

In this paper, we study the generalized Jacobi translation constructed by the Jacobi operator. Using the generalized Jacobi translation, we define generalized modulus of smoothness in the space L2(R+,Δα,β(t)dt). Equivalence is stated between the modulus of smoothness and the K-Functional constructed by the Sobolev space corresponding to the Jacobi operator.