Abstract
In this paper we prove some fixed point theorems by dropping the continuity requirement of convex contraction mappings introduced by Vasile I. Istratescu [Fixed point theory: An introduction, Mathematics and Its Applications, Vol. 7, D. Reidel Publishing Company, Dordrecht, Holland, 1981]. Further, we show that convex contraction mappings are strong enough to generate a fixed point but do not force the mapping to be continuous at the fixed point. Our work generalizes and unifies some well-known fixed point theorems due to Banach-Picard-Caccioppoli, Kannan and Reich.