Table of Contents
ISRN Applied Mathematics
Volume 2013 (2013), Article ID 379498, 4 pages
http://dx.doi.org/10.1155/2013/379498
Research Article

Nearly Contraction Mapping Principle for Fixed Points of Hemicontinuous Mappings

Department of Mathematics and Statistics, University of Maiduguri, Maiduguri, Nigeria

Received 20 May 2013; Accepted 13 August 2013

Academic Editors: M. Hermann and K. Karamanos

Copyright © 2013 Xavier Udo-utun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We extend the application of nearly contraction mapping principle introduced by Sahu (2005) for existence of fixed points of demicontinuous mappings to certain hemicontinuous nearly Lipschitzian nonlinear mappings in Banach spaces. We have applied certain results due to Sahu (2005) to obtain conditions for existence—and to introduce an asymptotic iterative process for construction—of fixed points of these hemicontractions with respect to a new auxiliary operator.