Browse > Article

MODIFIED MANN'S ALGORITHM BASED ON THE CQ METHOD FOR PSEUDO-CONTRACTIVE MAPPINGS  

Yao, Yonghong (Department of Mathematics, Tianjin Polytechnic University)
Zhou, Haiyun (Department of Mathematics, Shijiazhuang Mechanical Engineering College)
Liou, Yeong-Cheng (Department of Information Management, Cheng Shiu University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.5_6, 2010 , pp. 1499-1506 More about this Journal
Abstract
IIn this paper, we suggest and analyze a modified Mann's algorithm based on the CQ method for pseudo-contractive mappings in Hilbert spaces. Further, we prove a strong convergence theorem according to the proposed algorithm for pseudo-contractive mappings.
Keywords
Mann's algorithm; CQ method; pseudo-contractive mapping; strong convergence; fixed point;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 H.Y. Zhou, Convergence theorems of common fixed points for a finite family of Lipschitz pseudo-contractions in Banach spaces, Nonlinear Anal. 68(2008), 2977-2983.   DOI   ScienceOn
2 M.A. Noor, Some developments in general variational inequalities, Appl. Math. Comput. 152(2004), 199-277.   DOI   ScienceOn
3 M.A. Noor, Principles of Variational Inequalities, Lap-Lambert Academic Publishing AG and Co, Saarbrucken, Germany, 2009.
4 Y. Yao, Y.C. Liou and S.M. Kang, An iterative algorithm for asymptotically nonexpansive mappings, J. Appl. Math. and Informatics, 28(2010), No. 1-2, 75-86.   과학기술학회마을
5 J. Kang and Y. Su, Approximation methods for finite family of nonspreading mappings and nonexpansive mappings in Hilert spaces, J. Appl. Math. and Informatics, 28(2010), No. 1-2, 87-98.   과학기술학회마을
6 R. Ahmad and F. Usman, System of mixed variational inequalities in reflexive Banach spaces, J. Appl. Math. and Informatics, 27(2009), No. 3-4, 693-702.   과학기술학회마을
7 J. Schu, Approximating fixed points of Lipschitzian pseudo-contractive mappings, Houston J. Math. 19(1993), 107-115.
8 A. Udomene, Path convergence, approximation of fixed points and variational solutions of Lipschitz pseudo-contractions in Banach spaces, Nonlinear Anal. 67(2007), 2403-2414.   DOI   ScienceOn
9 C.H. Morales, On the fixed-point theory for local k-pseudo-contractions, Proc. Amer. Math. Soc. 81(1981), 71-74.
10 L.C. Zeng, N.C. Wong and J.C. Yao, Strong convergence theorems for strictly pseudo-contractive mappings of Browder-Petryshyn type, Taiwanese J. Math. 10(2006), 837-849.
11 Y. Yao, Y.C. Liou and R. Chen, Strong convergence of an iterative algorithm for pseudo-contractive mapping in Banach spaces, Nonlinear Anal. 67(2007), 3311-3317.   DOI   ScienceOn
12 C.E. Chidume and S.A. Mutangadura, An example on the Mann iteration method for Lipschitz pseudo-contractions, Proc. Amer. Math. Soc. 129(2001), 2359-2363.   DOI   ScienceOn
13 C.E. Chidume and M. Chika, Fixed point iteration for pseudo-contractive maps, Proc. Amer. Math. Soc. 127(1999), 1163-1170.   DOI   ScienceOn
14 G. Marino and H.K. Xu, Weak and strong convergence theorems for strictly pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329(2007), 336-349.   DOI   ScienceOn
15 K. Deimling, Zeros of accretive operators, Manuscripta Math. 13(1974), 365-374.   DOI
16 M.O. Osilike and A. Udomene, Demiclosedness principle and convergence theorems for strictly pseudo-contractive mappings of Browder-Petryshyn type, J. Math. Anal. Appl. 256(2001), 431-445.   DOI   ScienceOn
17 C.E. Chidume, Iterative approximation of fixed points of Lipschitz pseudo-contractive maps, Proc. Amer. Math. Soc. 129(2001), 2245-2251   DOI   ScienceOn
18 C.E. Chidume and H. Zegeye, Approximate fixed point sequences and convergence theorems for Lipschitz pseudo-contractive maps, Proc. Amer. Math. Soc. 132(2003), 831-840.
19 F.E. Browder and W.V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl.20(1967), 197-228   DOI
20 C.H. Morales and J.S. Jung, Convergence of paths for pseudo-contractive mappings in Banach spaces, Proc. Amer. Math. Soc. 128(2000), 3411-3419.   DOI   ScienceOn
21 C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems 20(2004), 103-120.   DOI   ScienceOn
22 T.H. Kim and H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61(2005), 51-60.   DOI   ScienceOn
23 C. Matinez-Yanes and H.K. Xu, Strong convergence of the CQ method for fixed point processes, Nonlinear Anal. 64(2006), 2400-2411.   DOI   ScienceOn
24 K. Nakajo and W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279(2003), 372-379.   DOI   ScienceOn
25 N. Shioji and W. Takahashi, Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces, Proc. Amer. Math. Soc. 125(1997), 3641-3645.   DOI   ScienceOn
26 S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 67(1979), 274-276.   DOI