Investigation of a new Jungck-type fixed point iteration method

Banach Contraction Principle, one of the well-known theorems in fixed point theory, has been generalized by many researchers and fixed point theorems have been obtained on different types of structures from normed spaces to Banach spaces. In this study, Jungck Contraction Principle, which is one of the remarkable generalizations of Banach Contraction Principle, was used. This thesis consists of four parts. In the first chapter, the historical development of the fixed point theory is given. In the second part, the basic concepts that will be used later are given. In the third chapter, the new iteration method is introduced and fixed point theorems such as convergence, stability, rate of convergence and data dependency are obtained by using a certain mapping class for this method. In the fourth chapter, the results obtained in this thesis study are summarized and possible future studies are given.