Equivalence of K-Functionals and Modulus of Smoothness Generated by a Generalized Dunkl Operator on the Real Line

Reem Fahad Al Subaie¹, Mohamed Ali Mourou^2*

¹Department of Mathematics, College of Sciences for Girls, University of Dammam, Dammam, Kingdom of Saudi Arabia.
²Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia.

DOI: 10.4236/apm.2015.56035                

Abstract

This paper is intended to establish the equivalence between K-functionals and modulus of smoothness tied to a Dunkl type operator on the real line.

Keywords

Differential-Difference Operator, Generalized Fourier Transform, Generalized Translation Operators, K-Functionals, Modulus of Smoothness

Conflicts of Interest

The authors declare no conflicts of interest.

References

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