Application of a Fixed Point of Derivative Function

Abstract

In \(\mathbb{R}\), the Brouwer’s fixed point theorem states that for any continuous functions \(\mathit{f}\) : [0,1] \(\rightarrow\) [0,1] has a fixed point. There is observing the nature of its functions, the domain of the function, or a support function. In this article, we show that the derivative function on [0,1] into itself has a fixed point even though the derivative function does not necessarily continuous.