THE FIXED POINT OF DERIVATIVE
MOHAMAD MUSLIKH *
Department of Mathematics,University Brawijaya, Malang 65143, Indonesia
ADEM KILICMAN
Department of Mathematics, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia
*Author to whom correspondence should be addressed.
Abstract
In ℝ, the Brouwer's fixed point theorem states that for any continuous functions f : [0, 1] → [0, 1] has a fixed point. 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.
Keywords: Fixed point, derivative