On the generalized Mellin integral operators

Abstract

In this study, we give a modification of Mellin convolution-type operators. In this way, we obtain the rate of convergence with the modulus of the continuity of the mmth-order Mellin derivative of function ff, but without the derivative of the operator. Then, we express the Taylor formula including Mellin derivatives with integral remainder. Later, a Voronovskaya-type theorem is proved. In the last part, we state order of approximation of the modified operators, and the obtained results are restated for the Mellin-Gauss-Weierstrass operator.

Keywords

• convolution operators
• mellin derivatives
• logarithmic modulus of continuity
• mellin-gauss-weierstrass operator
• 41a36
• 41a25