Quantitative Approximation Properties for Iterates of Moment Operator

Abstract

Here we state a quantitative approximation theorem by means of nets of certain modified Hadamard integrals, using iterates of moment type operators, for functions f defined over the positive real semi-axis ]0, +∞[, having Mellin derivatives. The main tool is a suitable K-functional which is compatible with the structure of the multiplicative group ]0, +∞[. Some numerical examples and graphical representations are illustrated.

Keywords:

• iterates of moment kernel
• Mellin derivatives
• generalized Hadamard integrals
• K –functional

AMS Subject Classification:

• 41A35
• 41A25
• 47G10