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Iteration processes for approximating fixed points of operators of monotone type

Published online by Cambridge University Press:  17 April 2009

Shih-Sen Chang  and
Kok-Keong Tan
Shih-Sen Chang
Affiliation:
Department of MathematicsSichuan University, ChengduSichuan 610064China
Kok-Keong Tan
Affiliation:
Department of MathematicsStatisticsand Computing ScienceDalhousie University, HalifaxNova ScotiaCanadaB3H 3J5
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Abstract

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In this paper, the unique fixed points of multi-valued and single-valued operators of monotone type are approximated by Ishikawa iteration processes or Mann and Ishikawa iteration processes with errors in uniformly smooth Banach spaces. The operators may not satisfy the Lipschitzian conditions and the domain or the range of the operators may not be bounded. The results presented improve and extend some recent results.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 433 - 445
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Chang, Shih-sen, ‘Some problems and results in the study of nonlinear analysis’, Nonlinear Anal. 30 (1997), 4197–4208.CrossRefGoogle Scholar
[2]Chidume, C.E., ‘Iterative construction of fixed points for multi-valued operators of the monotone type’, Appl. Anal. 23 (1986), 209–218.CrossRefGoogle Scholar
[3]Chidume, C.E., ‘Approximation of fixed points of strongly pseudo-contractive mappings’, Proc. Amer. Math. Soc. 120 (1994), 545–551.CrossRefGoogle Scholar
[4]Chidume, C.E., ‘Iterative solution of nonlinear equations with strongly accretive operators’, J. Math. Anal. Appl. 192 (1995), 502–518.CrossRefGoogle Scholar
[5]Deng, L. and Ding, X.P., ‘Iterative approximation of Lipschitz strictly pseudo-contractive mappings in uniformly smooth Banach spaces’, Nonlinear Anal. 24 (1995), 981–987.CrossRefGoogle Scholar
[6]Dunn, J.C., ‘Iterative construction of fixed points for multi-valued operators of the monotone type’, J. Funct. Anal. 27 (1978), 38–50.CrossRefGoogle Scholar
[7]Liu, L.S., ‘Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces’, J. Math. Anal. Appl. 194 (1995), 114–125.CrossRefGoogle Scholar
[8]Osilike, M.O., ‘Stable iteration procedures for strong pseudo-contractions and nonlinear operator equations of the accretive type’, J. Math. Anal. Appl. 204 (1996), 677–692.CrossRefGoogle Scholar
[9]Smul'yan, V.L., ‘Sur les topologies differentes dans l'espace de Banach’, C.R. Acad. Sci. URSS 23 (1939), 331–334.Google Scholar
[10]Smul'yan, V.L., ‘Sur la derivabilite de la norm dans l'espace de Banach’, C.R. Acad. Sci. URSS 27 (1940), 255–258.Google Scholar
[11]Tan, K.K. and Xu, H.K., ‘Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces’, J. Math. Anal. Appl. 178 (1993), 9–21.CrossRefGoogle Scholar