Approximation properties of bivariate extension of blending type operators

Abstract

The present article is in the continuation of our previous work (arXiv:2006.02669v1), where we have improved the order of approximation of $\alpha-$Bernstein P\u{a}lt\u{a}nea operators. In the given note, we study the bivariate extension of first order modification of these operators and their approximation properties such as convergence, error of approximation in terms of complete and partial modulus of continuity and their asymptotic formula. We present numerical examples to show the convergence of functions of two variables with the help of MATLAB software. Also, we construct the GBS operators associated to the bivariate extension and present their approximation behavior.