Fixed and periodic points under contraction mappings in metric spaces

Abstract

The main aim of this thesis is to investigate fixed and periodic points under contraction or distance shrinking mappings in metric spaces. -- Various situations are explored where the notion of contraction is relaxed and suitable modifications made on the metric space to ensure fixed or periodic points for the contraction. -- During the course of these investigations a few new results which guarantee fixed or periodic points for contractions under suitably weak conditions have been given for metric spaces. -- A few fixed point theorems have been also given in generalized complete metric spaces. Some of these are generalizations of well known results in this space. -- Convergence of a sequence of contractions and their fixed points have been studied briefly and a few new theorems have been added. -- In the end an attempt is made to apply the contraction mapping principle to the theory of differential and integral equations.