Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 186874, 14 pages
doi:10.1155/2010/186874
Research Article

Convergence Theorems on Asymptotically Pseudocontractive Mappings in the Intermediate Sense

Xiaolong Qin,1 Sun Young Cho,2 and Jong Kyu Kim3

1Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China
2Department of Mathematics, Gyeongsang National University, Jinju 660-701, South Korea
3Department of Mathematics Education, Kyungnam University, Masan 631-701, South Korea

Received 15 October 2009; Revised 8 January 2010; Accepted 23 February 2010

Academic Editor: Tomonari Suzuki

Copyright © 2010 Xiaolong Qin 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

A new nonlinear mapping is introduced. The convergence of Ishikawa iterative processes for the class of asymptotically pseudocontractive mappings in the intermediate sense is studied. Weak convergence theorems are established. A strong convergence theorem is also established without any compact assumption by considering the so-called hybrid projection methods.