On fixed point theorems in various metric spaces

Fixed point theory is one of the important topics of today's theory developing modern mathematics. Recently, several generalizations of the fixed point theory have been studied. One of these studies is the concept of z-metric space given by Jleli and Samet [13]. In this thesis, firstly z-metric space and some metric and topological properties are defined. Then, a new common fixed point theory for four mappings satisfying commuting mappings in this kind of spaces is proved and its results are given. These main results are z-metric version of Fisher's main theorem [7] and [8]. Furthermore, a generalization of Theorem 4 given by Mitrovic et al in [18] is introduced in z-metric spaces. Keywords: Fixed point, z-metric space, commuting mapping