A Study on Contraction Mappings and Fixed Point Theorems

Abstract

The thesis comprises of six chapters. The named Preliminaries, covers five sections. It is introductory and attempted to give a brief account of the historical developments of the subject and preliminary concepts used throughout the thesis. newline Fixed Point Theorem in Menger Space contains three sections. In section, a fixed point theorem for six self-maps has been proved which generalizes the result of Jain et al. We also give examples in support of our result. newline Fixed Point Theorem in Non-Archimedean Menger PM-Space comprises of three sections. In Section, we prove a unique common fixed point theorem for four self maps in non-Archimedean Menger PM-spaces. Our result improves the result of Singh, Dimri and Bhatt newline Fixed Point Theorem in Fuzzy Metric Space , describes three sections. In Section, the concept of semi-compatibility and occasionally weak compatibility in Fuzzy metric space has been applied to prove a common fixed point theorem which generalizes the result of Agarwal et.al. newlineEntitled Fixed Point Theorems using Sub-compatible Mappings in Fuzzy Metric Space , includes four sections. In Section, the concept of semi-compatibility and occasionally weakly compatibility in fuzzy metric space has been applied to prove common fixed point theorems for four self maps. Our result generalizes the result of Aage et. al. In Section 4, the concept of sub-compatibility, occasionally weakly compatibility and sub sequentially continuous mapping in Fuzzy metric space has been applied to prove a common fixed point theorem. We generalize the result of Agarwal et.al. newline Fixed Point Theorem in Cone Metric Space contains three sections. In section, we prove common fixed point theorems for faintly compatible and subsequently continuous mappings satisfying general contractive condition in cone metric spaces. Our result extend and generalize results of Badshah et.al. newline