Some fixed point results for single-valued and multivalued F-contraction mappings in metric space

This thesis consists of four chapters. The first chapter is dedicated to the introduction and literature review. The second chapter, titled 'Materials and Methods,' is subdivided into five sections. In these subsections, fundamental definitions, concepts, and theorems related to metric spaces are presented, along with discussions on certain topological concepts. Additionally, some single-valued and set-valued fixed point theorems in metric spaces are also addressed. The third chapter is divided into two subsections. The first subsection focuses on the sequential F-contraction mapping in ordered metric spaces, while the second subsection examines fixed point theorems for set-valued (α,F)-contraction mappings with α-admissible and τ-contraction values in metric spaces. The fourth chapter provides conclusions derived from our problems and suggests contributions to the literature based on these results.