Fixed point theorems using function classes in some metric spaces

In this thesis, fixed point theorems in various metric spaces using function classes are given in fiveth main sections. In the first introduction, fixed point definition, the history of fixed point theorems and their usage areas are mentioned. In the second part of the general information, metric space, semi-metric space, rectangular metric space, partial metric space and partial ordered metric space definitions and examples are found. In the third part, definitions and theorems are given, and rectangular semi-metric space definitions are given. In the fourth part, complete partial ordered rectangular semi-metric space is shown with full semi-rectangular semi-metric space and class functions. As a result, fixed point theorems have been proved by using class functions in mixed monotone mapping in rectangular semi-metric rectangles.