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Equivalence of <i>K</i>-Functionals and Modulus of Smoothness Generated by a Generalized Dunkl Operator on the Real Line
Department of Mathematics, College of Sciences for Girls, University of Dammam, Dammam, Kingdom of Saudi Arabia
Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia
- 1 Department of Mathematics, College of Sciences for Girls, University of Dammam, Dammam, Kingdom of Saudi Arabia
- 2 Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia
Advances in Pure Mathematics·Volume 05 (2015)·Pages 367–376·Published 5 May 2015·DOI10.4236/apm.2015.56035
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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.
KeywordsDifferential-Difference OperatorGeneralized Fourier TransformGeneralized Translation OperatorsK-FunctionalsModulus of Smoothness
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