- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 264909, 9 pages
A New Iterative Scheme of Modified Mann Iteration in Banach Space
College of Applied Mathematics, Chengdu University of Information Technology, No. 24, Block 1, Xuefu Road, Chengdu 610225, China
Received 5 October 2013; Revised 28 December 2013; Accepted 29 December 2013; Published 11 February 2014
Academic Editor: Sehie Park
Copyright © 2014 Jinzuo Chen 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.
- F. E. Browder, “Fixed-point theorems for noncompact mappings in Hilbert space,” Proceedings of the National Academy of Sciences of the United States of America, vol. 53, pp. 1272–1276, 1965.
- K. Goebel and W. A. Kirk, “A fixed point theorem for asymptotically nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 35, pp. 171–174, 1972.
- W. R. Mann, “Mean value methods in iteration,” Proceedings of the American Mathematical Society, vol. 4, pp. 506–510, 1953.
- F. E. Browder and W. V. Petryshyn, “Construction of fixed points of nonlinear mappings in Hilbert space,” Journal of Mathematical Analysis and Applications, vol. 20, pp. 197–228, 1967.
- C. Byrne, “A unified treatment of some iterative algorithms in signal processing and image reconstruction,” Inverse Problems, vol. 20, no. 1, pp. 103–120, 2004.
- B. Halpern, “Fixed points of nonexpanding maps,” Bulletin of the American Mathematical Society, vol. 73, pp. 957–961, 1967.
- T.-H. Kim and H.-K. Xu, “Strong convergence of modified Mann iterations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 61, no. 1-2, pp. 51–60, 2005.
- K. Nammanee, M. A. Noor, and S. Suantai, “Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 314, no. 1, pp. 320–334, 2006.
- S. Reich, “Weak convergence theorems for nonexpansive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 67, no. 2, pp. 274–276, 1979.
- H. F. Senter and W. G. Dotson, Jr., “Approximating fixed points of nonexpansive mappings,” Proceedings of the American Mathematical Society, vol. 44, pp. 375–380, 1974.
- H.-K. Xu, “Iterative algorithms for nonlinear operators,” Journal of the London Mathematical Society, vol. 66, no. 1, pp. 240–256, 2002.
- J. Schu, “Weak and strong convergence to fixed points of asymptotically nonexpansive mappings,” Bulletin of the Australian Mathematical Society, vol. 43, pp. 153–159, 1991.
- Y. J. Cho, H. Y. Zhou, and G. T. Guo, “Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings,” Computers & Mathematics with Applications, vol. 47, no. 4-5, pp. 707–717, 2004.
- K. S. Kim, “Approximating common fixed points of nonspreading-type mappings and nonexpansive mappings in a Hilbert space,” Abstract and Applied Analysis, vol. 2012, Article ID 594218, 18 pages, 2012.
- V. Barbu, Nonlinear Semi-Groups and Differential Equations in Banach Space, Noordhoff, Leiden, The Netherlands, 1976.