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The aim of this paper is to study a bivariate version of the operator investigated in [2], [4]. We shall present Voronovskaya type theorem and theorems giving a rate of convergence of this operator. Some applications for the limit problem are indicated.

Starting from a differential equation $\frac{\partial }{\partial t}W(\lambda ,t,u)=\frac{\lambda (u-t)}{p\left(t\right)}W(\lambda ,t,u)-\beta W(\lambda ,t,u)$ for the kernel of an operator $S_{\lambda }(f,t)={\int }_A^{B}W(\lambda ,t,u)f\left(u\right)du$ with the normalization condition ${\int }_A^{B}W(\lambda ,t,u)du=1$ we prove some properties which are similar to properties proved by Ismail and May for the exponential operators. In particular, we show that all these operators are approximation operators. Moreover, a method of determining $S_{\lambda }$ for a given function $p$ is introduced.

In this paper we will study some approximate properties of Baskakov-Durrmeyer type operators $M_n^{\alpha ,a}$. We determine the rate of convergence and prove the Voronovskaya type theorem for those operators.

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