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Ishikawa's iterations of real Lipschitz functions

Published online by Cambridge University Press:  17 April 2009

Lei Deng  and
Xie Ping Ding
Lei Deng
Affiliation:
Department of Mathematics, Chongqing Teacher's College Yongchuan, 632168, Sichuan, People's Republic of China
Xie Ping Ding
Affiliation:
Department of Mathematics, Sichuan Normal University, Chengdu 610066, Sichuan, People's Republic of China
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Abstract

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In this paper, we consider Ishikawa's iteration scheme to compute fixed points of real Lipschitz functions. Two general convergence theorems are obtained. Our results generalise the result of Hillam.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 1 , August 1992 , pp. 107 - 113
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Bailey, D.F., ‘Krasnoselski's theorem on the real line’, Amer. Math. Monthly 81 (1974), 506–507.CrossRefGoogle Scholar
[2]Hillam, B.P., ‘A generalization of Krasnoselski's theorem on the real line’, Math. Mag. 48 (1975), 167–168.CrossRefGoogle Scholar
[3]Ishikawa, S., ‘Fixed points by a new iteration method’, Proc. Amer. Math. Soc. 44 (1974), 147–150.CrossRefGoogle Scholar
[4]Krasnoselski, M.A., ‘Two remarks on the method of successive approximations’, Uspehi Math. Nauk 10 (1955), 123–127.Google Scholar
[5]Rhoades, B.E., ‘Comments on two fixed point iteration methods’, J. Math. Anal. Appl. 56 (1976), 741–750.CrossRefGoogle Scholar