Some new fixed point results for convex contractions in B-metric spaces

Abstract

The purpose of this paper is to consider various results for convex contraction mappings in the context of B-metric spaces. We, among other things, generalize, extend, correct and enrich the recent published results from the context of convex contractions defined on an ordinary metric spaces to the ones on the so-called B-metric spaces. One example shows that this generalization is genuine. Let us note that this paper represents only the beginning of our investigation of the properties of convex contractions observed in any general metric space. In the papers that are to be published, our considerations are applied to cone metric spaces, partial metric spaces, G-metrics, GB-metrics, extended B-metric spaces and many others.