Contraction mapping classes and fixed point theorems

Banach fixed point theorem (Contraction mapping principle) is a very good tool for the existence and uniqueness of the solution of problems in mathematics. Therefore, fixed point theory has been expanded and generalized by many researchers. In parallel with these developments, many contraction mappings have been introduced to the literature. This thesis consists of four chapters. In the first chapter, general information about fixed point theory and contraction mappings is given. In the second chapter, the basic definitions and theorems of functional analysis are given. The third chapter consists of thirteen sections. Here, the definition of contraction mapping classes, which have a wide application area in the literature, is examined with examples. Additionally, fixed point theorems proven by these contraction mappings are given. The last chapter includes conclusions and recommendations.