P-contractive mappings on metric spaces and some fixed point

In this thesis, firstly, a brief overview of the historical development of fixed-point theory is provided. To facilitate the understanding of the thesis, some important definitions, theorems, and examples that will be used to express and prove our results, along with studies in the literature, are given. Then, the concept of the new P-contraction transformation in metric spaces is introduced. Some examples are used to demonstrate the independence of P-contraction transformations in metric spaces. The concept of Suzuki-type P-contraction transformation is introduced, and a more general result of the famous Edelstein fixed-point theorem for such mappings on compact metric spaces is obtained.