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http://dx.doi.org/10.4134/JKMS.2003.40.1.029

ALMOST STABILITY OF THE MANN ITERATION METHOD WITH ERRORS FOR STRICTLY HEMI-CONTRACTIVE OPERATORS IN SMOOTH BANACH SPACES  

Liu, Z. (Department of Mathematics Liaoning Normal University)
Kang, S.M. (Department of Mathematics Gyeongsang National University)
Shim, S.H. (Department of Mathematics Gyeongsang National University)
Publication Information
Journal of the Korean Mathematical Society / v.40, no.1, 2003 , pp. 29-40 More about this Journal
Abstract
Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : KlongrightarrowK be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. The results presented in this paper generalize the corresponding results in [l]-[7], [20] and others.
Keywords
Mann iteration method with errors; strictly hemi-contractive operators; strongly pseudocontractive operators; local strongly pseudocontractive operators; smooth Banach spaces;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 7
연도 인용수 순위
1 Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations /
[ Y. Xu ] / J. Math. Anal. Appl.   DOI   ScienceOn
2 Iterative solutions of nonlinear equations with strongly accretive operators /
[ C. E. Chidume ] / J. Math. Anal. Appl.   DOI   ScienceOn
3 Approximation of fixed points of strongly pseudo-contractive mappings /
[ C. E. Chidume ] / Proc. Amer. Math. Soc.   DOI   ScienceOn
4 Iterative approximation of fixed points of Lipschitzian strictly pseudo-contractive mappings /
[ C. E. Chidume ] / Proc. Amer. Math. Soc.   DOI   ScienceOn
5 Comments on two fixed point iteration methods /
[ B. E. Rhoades ] / J. Math. Anal. Appl.   DOI   ScienceOn
6 Iterative approximation of fixed points for ф-hemicontractive operators in arbitrary Banach spaces /
[ Z. Liu;S. M. Kang ] / Acta Sci. Math. (Szeged)
7 Fixed point theory and stability results for fixed point iteration procedures /
[ A. M. Harder ] / Ph. D. Thesis, University of Missouri-Rolla
8 Convergence theorems for ф-strongly accretive and ф-hemicontractive operators /
[ Z. Liu;S. M. Kang ] / J. Math. Anal. Appl.   DOI   ScienceOn
9 Fixed point iteration for local strictly pseudo-contractive mapping /
[ X. Weng ] / Proc. Amer. Math. Soc.   DOI   ScienceOn
10 Some problems and results in the study of nonlinear analysis /
[ S. S. Chang ] / Nonlinear Anal. TMA   DOI   ScienceOn
11 A stable iteration procedure for nonexpansive mappings /
[ A. M. Harder;T. L. Hicks ] / Math. Japon.
12 Stable iteration procedures for strong pseudocontractions and nonlinear operator equations of the accretive type /
[ M. O. Osilike ] / J. Math. Anal. Appl.   DOI   ScienceOn
13 Mann iteration process for the fixed point of strictly pseudocontractive mapping in some Banach spaces /
[ J. A. Park ] / J. Korean Math. Soc.   과학기술학회마을
14 Mean value methods in iteration /
[ W. R. Mann ] / Proc. Amer. Math. Soc.   DOI   ScienceOn
15 Iterative construction of fixed points of strictly pseudocontractive mappings /
[ J. Schu ] / Applicable Anal.   DOI   ScienceOn
16 Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces /
[ S. S. Chang;Y. J. Cho;B. S. Lee;S. M. Kang ] / J. Math. Anal. Appl.   DOI   ScienceOn
17 Stability results for fixed point iteration procedures /
[ A. M. Harder;T. L. Hicks ] / Math. Japon.
18 Convergence and stability of the Ishikawa iteration procedures with errors for nonlinear equations of the ф-strongly accretive type /
[ Z. Liu;S. M. Kang ] / Neural. Parallel & Sci. Comput.
19 Stability of Ishikawa iteration methods with erros for strong pseudo-contractions and nonlinear equations involving accretive operators in arbitrary real Banach spaces /
[ Z. Liu;S. M. Kang ] / Math. and Computer Modell   DOI   ScienceOn
20 Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces /
[ C. E. Chidume;M. O. Osilike ] / Numer. Funct. Anal. Optimiz.   DOI
21 Fixed points by a new iteration method /
[ S. Ishikawa ] / Proc. Amer. Math. Soc.   DOI   ScienceOn
22 Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings /
[ C. E. Chidume;M. O. Osilike ] / J. Math. Anal. Appl.   DOI   ScienceOn
23 Stable iteration procedures for nonlinear pseudocontractive and accretive operator in arbitrary Banach spaces /
[ M. O. Osilike ] / Indian J. pure appl. Math.
24 Stability of the Mann and Ishikawa iteration procedures for ф-strongly pseudocontractions and nonlinear equations of the ф-strongly accretive type /
[ M. O. Osilike ] / J. Math. Anal. Appl.   DOI   ScienceOn