Multidimensional Kantorovich modifications of exponential sampling series

Abstract

This paper is devoted to construction of multidimensional Kantorovich modifications of exponential sampling series, which allows to approximate suitable measurable functions by considering their mean values on just one section of the function involved. Approximation behaviour of newly constructed operators is investigated at continuity points for log-uniformly continuous functions. The rate of convergence of the series is presented for the same functions by means of logarithmic modulus of continuity. A Voronovskaja type theorem is also presented by means of Mellin derivatives.

Mathematics Subject Classification (2020):

• Primary: 41A25
• Secondary: 41A30
• 47A58

Key words:

• Exponential sampling series
• Kantorovich operators
• rate of convergence
• Voronovskaja type theorem