Generalization of a fixed point theorem of Suzuki type in complete convex space

Abstract

The aim of this paper is to generalize a fixed point theorem given by Popescu[20]. We also complement and extend some very recent results proved by Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008) 1861 - 1869]. We furnish an example to validate our result.