Fixed point theory and applications in modular spaces

In this thesis, firstly, the historical development of fixed point theory, basic definitions and theorems, extensions of Banach contraction, graph theory, quasi metric spaces, modular spaces and modular metric spaces are mentioned. Then, by removing the symmetry property of modular metric space, quasi modular metric space is defined and some topological properties are given. Suzuki  Berinde contraction mappings and generalized   ,  simulation contraction mappings are defined and common fixed point theorems are proved in non-Archimedean modular metric spaces. Fixed point theorems are obtained by using  implicit contractions in non-Archimedean modular metric spaces. Also, applications of obtained fixed point theorems to graph theory, UlamHyers stability, well  posedness problem and integral equations are given. Containing rational expressions  ,      contractions and generalized simulation contractions are defined and related fixed point theorems are obtained in non-Archimedean quasi modular metric spaces. Applications of these theorems to the generalized UlamHyers stability and graph theory are given. Keywords: Fixed point theory, Modular spaces, Simulation function, Suzuki contraction, Berinde contraction, Admissible mapping, Graph theory, Ulam Hyers stability