Study on Some Random Fixed Point Theorems for Fuzzy Metric Spaces

Abstract

Our thesis entitled Study on Some Random Fixed Point Theorems For Fuzzy Metric Spaces is divided into six chapters.First chapter is introductory and deals with the historical development of fixed point theory particularly. This chapter mainly aims at making the present text as self contained as possible.Second chapter of this thesis entitled Fixed Point Theorem use in Fuzzy Random Space deals with a common fixed point theorem In this chapter we are proving a common fixed point theorem for random fuzzy space using by the theory of fuzzy metric space and random space and we discuss existence results and give new various definitions and examples. Our theorems determine extension and generalizations of previous proved theorems of many authors. These results extend the work of several authors.Third Chapter entitled Some Random Fixed Point Theorem shows impact of faintly compatible maps and (E.A.) Property in modified Intuitionistic Probabilistic Metric Space , In this chapter, we define the concept of modified intuitionistic probabilistic metric space the common property of E.A. We will prove new theorems and examples using faintly compatible maps in modified intuitionistic probabilistic metric space. Our main goal is to use common property E.A. in new directions. Our results have proved some common fixed point theorem in modified intuitionistic Menger probabilistic metric space satisfying an implicit relation.Fourth Chapter of this thesis entitled Random fixed point theorem in Fuzzy 3- Metric Space shows impact of E.A. Property . The aim of this chapter is to establish impact of E.A. property in fuzzy 3-metric space and the condition for two pairs of weakly compatible maps under E.A. like property have unique common fixed point. Our main result E.A. concept properties, weak compatibility allocation. To show the validity of the main results. This results also applies contraction condition to identify the unique fixed points of Fuzzy 3-Metric Space.Fifth chapter namely Some Random Fixed-Point Theorem For Weakl