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Journal of Applied Mathematics
Volume 2014, Article ID 738150, 10 pages
http://dx.doi.org/10.1155/2014/738150
Research Article

Demiclosedness Principle for Total Asymptotically Nonexpansive Mappings in Spaces

1Department of Mathematics, Atilim University, İncek 06836, Ankara, Turkey
2Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia
3Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran

Received 30 October 2013; Revised 11 December 2013; Accepted 11 December 2013; Published 25 February 2014

Academic Editor: Naseer Shahzad

Copyright © 2014 Erdal Karapınar 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 prove the demiclosedness principle for a class of mappings which is a generalization of all the forms of nonexpansive, asymptotically nonexpansive, and nearly asymptotically nonexpansive mappings. Moreover, we establish the existence theorem and convergence theorems for modified Ishikawa iterative process in the framework of spaces. Our results generalize, extend, and unify the corresponding results on the topic in the literature.