Equivalence of K-functionals and modulus of smoothness generated by a Dunkl type operator on the interval $(-1, 1)$

Abstract

Our aim in this paper is to show that the modulus of smoothness and the $K$-functionals constructed from the Sobolev-type space corresponding to the Dunkl operator are equivalent on the interval $(-1,1)$.

Keywords

• Fourier–Dunkl series
• Dunkl transform
• generalized translation operator
• $K$-functionals
• modulus of smoothness