On bivariate Kantorovich exponential sampling series

Abstract

In this paper, we introduce and analyze the approximation properties of bivariate generalization for the family of Kantorovich type exponential sampling series. We derive the basic convergence result and Voronovskaya type theorem for the proposed sampling series. Using logarithmic modulus of smoothness, we establish the quantitative estimate of order of convergence for the Kantorovich type exponential sampling series. Furthermore, we study the convergence results for the generalized Boolean sum (GBS) operator associated with bivariate Kantorovich exponential sampling series. At the end, we provide a few examples of kernels to which the presented theory can be applied along with the graphical representation and error estimates.