Sabit nokta teorisinde küme değerli operatörler üzerine

Generalization of some concepts and theorems in fixed point theory has an important place. One of these generalizations consists of studies on set-valued operators. Accordingly, this thesis examines the applications of fixed point theory on set-valued operators. The thesis primarily addresses the basic concepts and definitions of fixed-point theory and set-valued operators. Then, various fixed-point theorems for these operators are examined. In this context, how theoretical results can be applied to practical problems is explained with examples. Then, convergence and data dependency results for the newly defined four-step iteration method and fixed-point concepts such as weak, strong convergence, stability and data dependency results under certain conditions for the set-valued version of this iteration method were proven. Important parts of these proofs are demonstrated with examples using MATHEMATICA and MATLAB programs. The thesis aims to contribute to the existing literature on this subject by emphasizing the importance of fixed-point theory and set-valued operators in mathematical analysis. It is hoped that this study will inspire research in this field by providing new perspectives on the practical applications of mathematical theories. Keywords: Fixed Point Theory, Set-Valued Operators, Iteration Methods, Stability, Data Dependency, Convergence