Existence of Fixed Points for Some Mappings in Various Generalized Metric Spaces

Abstract

The intent of this dissertation entitled “Existence of Fixed Points for Some Mappings in Various Generalized Metric Spaces” embodies a brief account of investigation carried out by authors on existence of fixed points of self mappings in various metric spaces under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics, 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 is one of the most powerful tool in nonlinear analysis. Fixed point theory has wide ranging application in many area of mathematics. For example, in finding the solution of the system of linear equations, in proving the existence of solutions of ordinary and partial differential equation, integral equations, analysis and many other disciplines. The whole work is 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 Fixed point theorem for α−ψ contractive mapping which guarantees the existence and uniqueness of fixed point in b-metric spaces. The aim of Chapter III is to study common fixed point results for weakly isotone increasing mapping in partially ordered b-metric-like space. Chapter IV is concerned with common fixed theorems using newly defined contractive type mappings for partially ordered b-metric-like space. Moreover, corollary is obtained in this chapter. At the end, we have have presented some references of research papers and books cited in the dissertation.