Different type metric spaces and fixed point results in these spaces

In this thesis, firstly some new notions such as T-orbitally w-completeness, orbitally w-continuity and almost weakly w-contractive mapping in the modular metric spaces are defined. Some fixed point theorems for these new concepts are proved and a homotopy application related to obtained results is given. Some fixed point theorems on complete modular S-metric spaces are proved by adding of modular S-metric spaces and their some properties to literature. The concept of modular ultrametric space is first defined and some fixed point theorems are given in modular spherically complete ultrametric space. Some fixed point results are given by introducing for the first time the modular b-metric spaces and an application for the systems of linear equations is performed. As a new concept in literature, C*-algebra-valued S-metric spaces are given and the version of Banach contraction mapping principle in this space is proved.