Fixed point theorems in fuzzy metric spaces and applications for integral equations

Fixed point theory has applications in many branches of science such as engineering, biology and statistics, as well as applied mathematics. With the development of the concept of fuzzy sets, fixed point theory has been developed on fuzzy sets and has found a wide application area. In this thesis, first the fundamental concepts about fuzzy set theory will be included. Then, the development of fixed point theory in fuzzy metric spaces will be discussed. Thus, fuzzy fixed point theorems along with fuzzy contraction mappings will be systematically investigated. Finally, studies on the application of these fixed point theorems to integral equations will be examined.