Approximation properties of bivariate sampling Durrmeyer series in weighted spaces of functions

D. Özer, M. Turgay, T. Acar

This paper deals with approximation properties of bivariate sampling Durrmeyer operators for functions belonging to weighted spaces of functions. After a short preliminaries and auxilary results we present well-definiteness of (S_w^ζ,ζ). Main results of the paper includes pointwise and uniform convergence of the family of operators, rate of convergence via bivariate weighted modulus of continuity and quantitative Voronovskaja type theorem.

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16,  supplement issue 3 (2023), pp. 89-107