Results on bivariate Szasz-Mirakyan type operators in polynomial weight spaces

Abstract

In this paper, bivariate Szász-Mirakjan type operators are introduced along with the estimation of its approximation properties and its rate of convergence. Furthermore, to check the asymptotic behavior of the said bivariate operators, Voronovskaya type theorem is proved and determined the simultaneous approximation of the operators for first order partial derivative. Finally, the convergence behavior of the bivariate operators are obtained through graphical representation and validated the numerical results with the results of Szász-Mirakjan operators for the function of two variables.

Approximation of associated GBS operators by Szasz-Mirakjan type operators

“…Yadav et al [49] proposed bivariate Szász-Mirakjan type operators for the function of two variables, where they studied the approximation properties as well as the rate of convergence of the proposed bivariate operators in a polynomial weighted space and obtained a Voronovskaya type theorem as well as discussed simultaneous approximation property for the bivariate operators. The bivariate Szász-Mirakjan type operators are considered for continuous and bounded functions on [0, ∞) × [0, ∞) as below:…”