The Equivalence Theorem for a K-Functional and a Modulus of Smoothness Constructed by a Singular Differential-Difference Operator on R
R. F. Al Subaie
Department of Mathematics, College of Sciences for Girls, University of Dammam, P.O.Box 1982, Dammam 31441, Saudi Arabia.
M. A. Mourou *
Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5019, Monastir, Tunisia.
*Author to whom correspondence should be addressed.
Abstract
The purpose of this article is to establish the equivalence between a K-functional and a modulus of smoothness generated by a Dunkl type operator on the real line.
Keywords: Differential-difference operator, generalized fourier transform, generalized translation operator, K-functional, Modulus of smoothness.