Generalized and special fixed point theorems in bipolar metric spaces

In this thesis study, it is aimed to describe generalizations of some fixed point theorems, which are well-known in literature, to bipolar metric spaces. For this purpose, first of all, the historical development of fixed point theory, metric spaces and bipolar metric spaces are briefly mentioned and some basic concepts and theorems, which can prepare for the study, are given. In addition, the definition of bipolar metric spaces is given and some definitions, theorems and results related to these spaces, which are used in the study, are expressed. Afterwards, in the main part of the study, important fixed point theorems such as coupled fixed point theorems and common fixed point theorems are generalized to bipolar metric spaces. The concepts such as (ε,λ)-uniform locally contraction mapping, weakly contraction mapping, α-ψ-contraction mapping, α-admissible mapping and multivalued mapping are defined on the studied spaces and the theorems and results showing the existence and uniqueness of the fixed point for these mappings are expressed.