Fixed point theorems in modular metric spaces and their applications

The concept of modular metric space is a generalized form of classical metric space. Since concepts such as convergence defined in this space are weaker than classical metric spaces, the results obtained in this space are more comprehensive. The purpose of modular metric spaces has been to obtain more general results on a weaker topological structure. In this thesis, modular metric space structure is focused on. The basic properties of modular metric space are reminded and its relation with metric spaces is expressed. Based on the basic fixed point theorems given in modular metric spaces, the structure of the mappings expected to have fixed points in these spaces is discussed. The existence of fixed points of Carist type, Feng- Liu type and ψ," " φ type mappings, which have an important place for multivalued mappings, in these spaces are shown. Finally, an application of Caristi type mappings for functional equations and Feng- Liu type mappings for differential equations are given.