On a general metric condition in fixed point theory

Abstract

The purpose of this talk is to present some new fixed point results for singlevalued and multivalued orbital (graph) contractions in complete metric spaces. We will consider existence results, as well as some stability properties (such as, data dependence, well-posedness in the sense of Reich and Zaslavski, Ostrowski stability and Ulam-Hyers stability) for the fixed point equation. We will also point out the role of the retraction-displacement condition in fixed point theory.