Approximating n-th differentiable functions of two variables and mid-point formula

Abstract

In this work, approximations for real two variables function $f$ which has continuous partial $(n-1)$-derivatives $(n \ge 1)$ and has the $n$--th partial derivative of bounded bivariation or absolutely continuous are established. Explicit bounds for this representation are given. An approximation of a function $f$ by its mid-point formula with its error is established.