Approximation properties of multivariate exponential sampling series

S. Kurşun; M. Turgay; O. Alagöz; T. Acar

doi:10.15330/cmp.13.3.666-675

S. Kurşun Selcuk University, Konya, Turkey https://orcid.org/0000-0001-6697-9627
M. Turgay Selcuk University, Konya, Turkey https://orcid.org/0000-0002-1953-1069
O. Alagöz Bilecik Şeyh Edebali University, 11230 Bilecik, Turkey
T. Acar Selcuk University, Konya, Turkey https://orcid.org/0000-0003-0982-9459

https://doi.org/10.15330/cmp.13.3.666-675

Keywords: multivariate exponential sampling series, rate of convergence, multivariate Mellin-Taylor formula, Voronovskaja theorem

Published online: 2021-12-07

Abstract

In this paper, we generalize the family of exponential sampling series for functions of $n$ variables and study their pointwise and uniform convergence as well as the rate of convergence for the functions belonging to space of $\log$-uniformly continuous functions. Furthermore, we state and prove the generalized Mellin-Taylor's expansion of multivariate functions. Using this expansion we establish pointwise asymptotic behaviour of the series by means of Voronovskaja type theorem.