Fixed points of contraction mappings on metric and G–Metric spaces

Abstract

The present dissertation entitled, “Fixed Points of Contraction Mappings on Metric and G-Metric Spaces”, contains a brief account of investigations carried out by various authors and by me on existence of fixed points of self mappings in metric space under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematices and Computer Applications, Thapar University, Patiala. The aim of this work is to study and obtain some result on existence and uniqueness of fixed points. Fixed point theory has wide ranging application in many areas of mathematics. For example, in finding the solution of the system of linear equations, in proving the existence of solutions of ordinary and differential equation, integral equations, analysis and many other disciplines. The whole work is divided into three 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 Contraction Theorem which guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces and applications of Banach Contraction Theorem to system of linear equations and integral equations. The aim of chapter III is to study fixed point results for mapping satisfying sufficient contractive conditions on a complete G - metric space and studied the existence and uniqueness of fixed points. Towards the end, references of various publications cited in the