Principle of contractive mappings and fixed point theorems in cone metric spaces

In this thesis, principle of contractive mappings and fixed point theorems in cone metric spaces have been investigated. First of all, background information, some basic definitions and theorems of fixed point theory were given for mappings in metric spaces. Secondly, definition, types and some properties of cone were given. Here, there are no normal cones with normal constant every regular cone is normal and for each there are cones with normal constant were investigated. Also definition and basic properties of cone metric spaces were given. Then some fixed point theorems have been investigated for the mappings which satisfy the contractive condition before under the assumption of normality in after that if it is possible by omitting the assumption of normality in . Also presence of coincidence and common fixed points of mappings which satisfy the contractive condition in cone metric spaces were investigated. Then characterization of best approximations and properties were given in cone metric spaces.Finally endpoints and fixed points of set-valued contractions were given and some fixed point theorems of these mappings were investigated.Key Words : Metric space, contractive mapping, cone, cone metricspace, fixed point, best approximations, set-valuedmappings