Some fixed point theorems in modular metric sapces

In this thesis, fundamental definitions of modular metric space concept and metric properties of this space which was given by Chistyakov [10,11,12] are investigated. Some basic fixed point theorems are given with the help of Chistyakov [13], Mongkolkeha, Sintunavarad, Kumam [14] and Cho, Saadati, Sadeghi [30] papers. Firstly, locally contraction, -uniformly locally contractive mappings, -chinable, weak contraction mapping concepts are defined and a fixed point theorem for these concepts is proved in complete modular metric spaces which was given by Kılınç and Alaca [25]. Further, by Kılınç and Alaca [27] some fixed point theorems for Ćirić type, the generalized contraction mappings are proved and the existence and uniqueness of common fixed point of a class of generalized contraction mappings are shown in these spaces. Later, some fixed point results for Meir and Keeler [29] type contractive condition on these spaces are given. These results are modular metric versions of the Ćirić [15,16], Meir and Keeler [29] and Reich's [33] results and the generalizations of earlier results of Kılınç and Alaca [25]. Finally, two main fixed point theorems for commuting mappings in modular metric spaces are proved. These results are modular metric versions of results of Jungck [20] and Fisher [19].