Fixed Point Theorems for Different Contraction Mappings

Abstract

The present dissertation entitled, "FIXED POINT THEOREMS FOR DIFFERENT CONTRACTION MAPPINGS", contains a study about Fixed point theory by me on existence of fixed points of self mappings in metric space under the supervision of Dr. Jatinderdeep Kaur, Associate Professor, School of Mathematics, Thapar Institute of Engineering and Technology, Patiala. The aim of this work is to study and obtain some result on existence and uniqueness of fixed points. Fixed point theory has been revealed as a very powerful and important tool in the study of non-linear analysis. Various problems in physics, chemistry, biology, economics etc. can be solved by maling use of fixed point theorems. The work presented in this dissertation has been divided into four chapters. Chapter I is introduction which includes brief account of definitions and results which will be required for the later chapters. In Chapter II, we have studied Banach fixed point theorem which guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces. Also, we present some fixed point theorems in compact metric space. The purpose of the Chapter III is to study fixed point theorems for generalized contraction mappings on a S-orbitally complete metric space and studied the existence and uniqueness of fixed points. In the Chapter IV, we have studied some fixed point theorems under quasi contraction condition. The purpose of this chapter is to extend the result presented in chapter III. At the end of the present dissertation, we have added bibliography.