- 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 2012 (2012), Article ID 926017, 15 pages
Minimum-Norm Fixed Point of Pseudocontractive Mappings
1Department of Mathematics, University of Botswana, Private Bag 00704, Gaborone, Botswana
2Department of Mathematics, King Abdulaziz University, P.O. Box. 80203, Jeddah 21589, Saudi Arabia
Received 7 May 2012; Accepted 14 June 2012
Academic Editor: Yonghong Yao
Copyright © 2012 Habtu Zegeye 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.
- R. P. Agarwal, D. ORegan, and D. R. Sahu, Fixed Point Theory for Lipschitzian-type Mappings with Applications, Springer, Dordrecht, The Netherlands, 2000.
- D. R. Sahu and A. Petruşel, “Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces,” Nonlinear Analysis, vol. 74, no. 17, pp. 6012–6023, 2011.
- Q. B. Zhang and C. Z. Cheng, “Strong convergence theorem for a family of Lipschitz pseudocontractive mappings in a Hilbert space,” Mathematical and Computer Modelling, vol. 48, no. 3-4, pp. 480–485, 2008.
- X. Yang, Y.-C. Liou, and Y. Yao, “Finding minimum norm fixed point of nonexpansive mappings and applications,” Mathematical Problems in Engineering, vol. 2011, Article ID 106450, 13 pages, 2011.
- 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.
- M. I. Sezan and H. Stark, “Applications of convex projection theory to image recovery in tomography and related areas,” in Image Recovery Theory and Applications, H. Stark, Ed., pp. 415–462, Academic Press, Orlando, Fla, USA, 1987.
- D. Youla, “Mathematical theory of image restoration by the method of convex projections,” in Image Recovery Theory and Applications, H. Stark, Ed., pp. 29–77, Academic Press, Orlando, Fla, USA, 1987.
- F. E. Browder, “Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces,” Archive for Rational Mechanics and Analysis, vol. 24, pp. 82–90, 1967.
- S. Reich, “Strong convergence theorems for resolvents of accretive operators in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 75, no. 1, pp. 287–292, 1980.
- W. Takahashi and Y. Ueda, “On Reich's strong convergence theorems for resolvents of accretive operators,” Journal of Mathematical Analysis and Applications, vol. 104, no. 2, pp. 546–553, 1984.
- C. H. Morales and J. S. Jung, “Convergence of paths for pseudocontractive mappings in Banach spaces,” Proceedings of the American Mathematical Society, vol. 128, no. 11, pp. 3411–3419, 2000.
- E. U. Ofoedu and H. Zegeye, “Further investigation on iteration processes for pseudocontractive mappings with application,” Nonlinear Analysis, vol. 75, no. 1, pp. 153–162, 2012.
- E. U. Ofoedu and H. Zegeye, “Iterative algorithm for multi-valued pseudocontractive mappings in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 372, no. 1, pp. 68–76, 2010.
- H. Zegeye, N. Shahzad, and T. Mekonen, “Viscosity approximation methods for pseudocontractive mappings in Banach spaces,” Applied Mathematics and Computation, vol. 185, no. 1, pp. 538–546, 2007.
- H. Zegeye, N. Shahzad, and M. A. Alghamdi, “Convergence of Ishikawa's iteration method for pseudocontractive mappings,” Nonlinear Analysis, vol. 74, no. 18, pp. 7304–7311, 2011.
- Y. Cai, Y. Tang, and L. Liu, “Iterative algorithms for minimum-norm fixed point of nonexpansive mapping in Hilbert space,” Fixed Point Theory and Applications, vol. 2012, p. 49, 2012.
- W. Takahashi, Nonlinear Functional Analysis, Kindikagaku, Tokyo, Japan, 1988.
- C. E. Chidume, H. Zegeye, and S. J. Aneke, “Approximation of fixed points of weakly contractive nonself maps in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 270, no. 1, pp. 189–199, 2002.
- H. Zegeye and N. Shahzad, “Convergence of Mann's type iteration method for generalized asymptotically nonexpansive mappings,” Computers & Mathematics with Applications, vol. 62, no. 11, pp. 4007–4014, 2011.
- K. Deimling, “Zeros of accretive operators,” Manuscripta Mathematica, vol. 13, pp. 365–374, 1974.
- C. E. Chidume and H. Zegeye, “Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps,” Proceedings of the American Mathematical Society, vol. 132, no. 3, pp. 831–840, 2004.
- L. Landweber, “An iteration formula for Fredholm integral equations of the first kind,” American Journal of Mathematics, vol. 73, pp. 615–624, 1951.