Maximality, Fixed Points and Variational Principles for Mappings on Quasi-Uniform Spaces

Abstract

By making use of maximality on some appropriate pre orderings, some classical results stated in the context of metric spaces are extended to spaces endowed with uniform structures. Indeed, various results on fixed point theory and variational principles have been proved by arguments using order relations in metric spaces. In this work, some of the mentioned results are extended to spaces having a uniform structure, by means of appropriate pre orderings. The concept of $w$ distance is used to this purpose. Moreover, equivalences of maximality are stated for general pre orderings.