The iterative solution of a class of nonlinear equation

Iteration methods in fixed point theory, have a wide literatüre, and the results obtained for these methods can be listed as the convergence of the sequence obtained from the mentioned iteration method, the rate of convergence, the equivalence of convergence, data dependence, and stability. In addition, these methods are used as an effective tool in reaching the solution of integral or differential equations. This thesis consists of five chapters. In the first chapter, a summary of the literature on fixed point theory is given. In the second chapter, the basic concepts, definitions, and theorems to be used in the thesis are given. In the third chapter, the convergence of the newly defined four-step fixed point iteration method and the rate of convergence were investigated under certain conditions by using the rational mapping class. In addition, the concepts of stability and data dependency were examined for the new iteration method. Also, nontrivial numerical examples are given for these results. In the fourth chapter, it is proved that the solution of a generalized type integral equation can be reached by using the new iteration method, and it is shown that the solution of this equation is data-dependent. In the fifth chapter, the results obtained during the thesis are mentioned and information about the possible future studies is given.