Fixed Points in Uniform Spaces

Abstract

We introduce notions of J-contractions and J-nonexpansive maps on a uniform space generated by a collection of pseudometrics which generalize Φ-contractions and j-nonexpansive maps, respectively. Fixed point theorems for J-contractions and J-nonexpansive maps under various conditions which cover Angelov’s results are presented, and some criteria for maps to be J-contractions and J-nonexpansive maps are also given. Furthermore, we investigate their fixed point sets using the concept of virtual stability and give some interesting examples.