Fixed point theory in various generalized metric-type spaces.

Abstract

In the theory of fixed points, there are numerous articles dealing with generalization of the basic Banach contraction mapping principle. There has been two lines of approach. The first one is concerned with generalizations of the contractive conditions on the mapping space. The other line of investigation deals with various generalizations of the metric spaces and the results that can be obtained in these new frameworks, referred to as metric-type spaces. In this thesis, we elected for the latter approach by providing a more general framework for a b-metric space , G-metric space and S-metric space. In this thesis, we proved that these new metric-type spaces equipped with various contractions type mappings have unique fixed points and provide numerous examples of each metric-type spaced mentioned.