- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 169410, 14 pages
The Equivalence of Convergence Results between Mann and Multistep Iterations with Errors for Uniformly Continuous Generalized Weak -Pseudocontractive Mappings in Banach Spaces
1Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
2Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China
Received 24 November 2012; Accepted 7 December 2012
Academic Editor: Jen-Chih Yao
Copyright © 2012 Guiwen Lv and Haiyun Zhou. 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.
- C. E. Chidume and M. O. Osilike, “Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces,” Numerical Functional Analysis and Optimization, vol. 15, no. 7-8, pp. 779–790, 1994.
- M. O. Osilike, “Stability of the Ishikawa iteration method for quasi-contractive maps,” Indian Journal of Pure and Applied Mathematics, vol. 28, no. 9, pp. 1251–1265, 1997.
- J. K. Kim, D. R. Sahu, and Y. M. Nam, “Convergence theorem for fixed points of nearly uniform L-Lipschitzian asymptotically generalized -hemicontractive mappings,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 12, pp. e2833–e2838, 2009.
- E. U. Ofoedu, “Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space,” Journal of Mathematical Analysis and Applications, vol. 321, no. 2, pp. 722–728, 2006.
- S. R. Wang, Z. H. Yang, and M. Xiong, “A note about: iterative approximation of fixed points for asymptotically nonexpansive type mappings with error member,” Acta Mathematica Sinica, vol. 51, no. 4, pp. 671–676, 2008 (Chinese).
- Y. S. Song and X. K. Chai, “Strong convergence theorems of viscosity approximation methods for generalized Lipschitz pseudocontractive mappings,” Acta Mathematica Sinica, vol. 51, no. 3, pp. 501–508, 2008 (Chinese).
- Y. J. Cho, J. I. Kang, and H. Y. Zhou, “Approximating common fixed points of asymptotically nonexpansive mappings,” Bulletin of the Korean Mathematical Society, vol. 42, no. 4, pp. 661–670, 2005.
- L. C. Zeng, “Iterative approximation of fixed points of asymptotically pseudo-contractive mappings in uniformly smooth Banach spaces,” Chinese Annals of Mathematics, vol. 26, no. 2, pp. 283–290, 2005 (Chinese).
- Z. Huang, “Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively -pseudocontractive mappings without Lipschitzian assumptions,” Journal of Mathematical Analysis and Applications, vol. 329, no. 2, pp. 935–947, 2007.
- C. E. Chidume and C. O. Chidume, “Convergence theorems for fixed points of uniformly continuous generalized -hemi-contractive mappings,” Journal of Mathematical Analysis and Applications, vol. 303, no. 2, pp. 545–554, 2005.
- F. Gu, “Some convergence theorems of non-implicit iteration process with errors for a finite families of I-asymptotically nonexpansive mappings,” Applied Mathematics and Computation, vol. 216, no. 1, pp. 161–172, 2010.
- R. X. Ni, “Equivalence between the convergences of multi-step iterations with errors for uniformly generalized Lipschitz continuous operators,” Journal of Systems Science and Mathematical Sciences, vol. 30, no. 3, pp. 398–409, 2010 (Chinese).
- S. S. Chang, “Some problems and results in the study of nonlinear analysis,” Nonlinear Analysis: Theory, Methods & Applications, vol. 30, no. 7, pp. 4197–4208, 1997.
- C. Moore and B. V. C. Nnoli, “Iterative solution of nonlinear equations involving set-valued uniformly accretive operators,” Computers & Mathematics with Applications, vol. 42, no. 1-2, pp. 131–140, 2001.