Results on bivariate  SzÃ¡sz-Mirakjan type operators in  polynomial weight spaces

Rishikesh Yadav; Ramakanta Meher; Vishnu Narayan Mishra

Rishikesh Yadav Sardar Vallabhbhai National Institute of Technology Surat, Surat-395 007, Gujarat, India.
Ramakanta Meher Sardar Vallabhbhai National Institute of Technology Surat, Surat-395 007, Gujarat, India.
Vishnu Narayan Mishra Indira Gandhi National Tribal University, Lalpur, Amarkantak-484 887, Anuppur, Madhya Pradesh, India.

Abstract

In this paper, bivariate Sz$\acute{\text{a}}$sz-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 Sz$\acute{\text{a}}$sz-Mirakjan operators for the function of two variables.