On bivariate Kantorovich exponential sampling series

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