On common fixed point theorems in various abstract spaces

Abstract

The present thesis entitled On Common Fixed Point Theorems In Various Abstract Spaces comprises certain investigations carried out by me at the Department Of Mathematics, Desh Bhagat University, Mandi Gobindgarh, under the supervision of Dr. Tejwant Singh and Dr. Saurabh Manro. newlineThe motive of this research is to extend, unify and generalize various results in different abstract spaces for various mappings such that compatible mappings, R-weakly commuting mappings and their different variants. newlineThe thesis consists of seven chapters. Chapter-I is introductory in nature, where we fix notations and terminology to be used in the subsequent chapters. In this chapter, some basic definitions, classical and recent results related to metric fixed point theory have been presented. Some of these results have been extended and generalized in the subsequent chapters. newline newlineIn Chapter-II some common fixed point theorems for variants of R-weakly commuting mappings in parametric S-metric spaces have been proved. The results presented in this chapter have been consequently improved and polished up many studied common fixed point theorems in the existing research. Also, some examples in support of these results have been given. newlineIn Chapter-III some common fixed point theorems for multi-valued operator on G- newlinemetric space have been proved with the help of method of Kikkawa. newline newlineThe objective of Chapter-IV is to prove common fixed point theorems in complete fuzzy metric space by using rational type contractive conditions. Here also, common fixed point theorem in an intuitionistic fuzzy metric space have been proved. newlineChapter-V, In this chapter, we prove some new common fixed point theorems in intuitionistic Menger metric spaces. While proving our results, we utilize the idea of compatibility due to Jungck together with conditionally reciprocal continuity due to newlineR. P. Pant and R. K. Bisht . Consequently, our results improve and sharpen many newline newline newline newlineknown common fixed point theorems available in the existing literature of intuitionistic menger fixed