PROVING FIXED POINT THEOREMS USING GENERAL PRINCIPLES

Abstract

This dissertation consists of four chapters. In chapter one we present a brief introduction to fixed point theory and the most important result in the fixed point theory is the famous theorem of Brouwer which says that the closed unit sphere of En has the fixed point property. Also we present some applications of fixed point.

In chapter two we present the concept of contraction, some generalization of the contraction mappings and an application of the contraction principle.

In chapter three B.E.Rhaodes proved fixed-point theorems using general principle. It is purpose to point that, all of fixed-point results are special cases either of general principle by Hick or Park or Rhoades.

The last chapter contains basic idea of 2-metric space. Many authors have studied the concept of fixed-point theory in 2-metric space. In this chapter M.S.Rathore and Usha Rani attempted a result in a complete 2-metric space which extends the result of Ganguly and Chandel.