On some Meir-Keeler type fixed point results

In this thesis, which consisting of seven chapters, new discontinuity results at the fixed point were obtained with the help of two different numbers used in the solution of Rhoades' open problem of discontinuity at the fixed point. In addition, in this study, new fixed circle and fixed disc results were obtained, inspired by Meir-Keeler and Caristi type contraction conditions. The first chapter of this thesis is the introduction. In the second chapter, the basic concepts and some examples that will be used throughout the study are given. In the third chapter, two different numbers used in the solution of Rhoades' open discontinuity problem are defined, and discontinuity results at the fixed point obtained with the help of these numbers are given. In the fourth chapter, the definition and examples of k-continuity are discussed and the results obtained with the help of k-continuity are given. In the fifth section, discontinuity results at the fixed point obtained using Meir-Keeler and Caristi type contraction conditions are given. In the sixth chapter, the fixed circle results obtained with the help of numbers used in the solution of Rhoades' open discontinuity problem are examined. Additionally, new fixed circle and fixed disc results obtained by the Meir-Keeler and Caristi method are given. In the seventh section, applications to various activation functions are given.