On Mellin convolution operators: a direct approach to the asymptotic formulae

Abstract

Here, using Mellin derivatives, a different notion of moment and a suitable modulus of continuity, we state a quantitative Voronovskaja approximation formula for a general class of Mellin convolution operators. This gives a direct approach to the study of pointwise approximation of such operators, without using the Fourier analysis and its results. Various applications to important specific examples are given.

Keywords:

• Mellin convolution operators
• Mellin derivatives
• moments
• modulus of continuity
• K-functional

AMS Subject Classifications::

• 41A35
• 41A25
• 47G10

Acknowledgements

We wish to thank the Referees for their valuable suggestions which have improved the paper.