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Generalization of Leader's fixed point principle

Published online by Cambridge University Press:  17 April 2009

Tanmoy Som  and
R.N. Mukherjee
Tanmoy Som
Affiliation:
Applied Mathematics Section, School of Applied Sciences, Institute of Technology, Banaras Hindu University, Varanasi 221005, India.
R.N. Mukherjee
Affiliation:
Applied Mathematics Section, School of Applied Sciences, Institute of Technology, Banaras Hindu University, Varanasi 221005, India.
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Abstract

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In J. Math. Anal. Appl. 61 (1977), 466–474, Leader has given a fixed point principle for an operator f:X → X, where X is a metric-space, based on conditional uniform equivalence of orbits. We generalize this principle for two mappings f1 and f2 to give common fixed point results in two different ways. Further we derive an f-generalized fixed point theorem for two commuting mappings.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 3 , June 1984 , pp. 349 - 356
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Leader, S., “Fixed points for operators on metric spaces with conditional uniform equivalence of orbits”, J. Math. Anal. Appl. 61 (1977), 466–474.CrossRefGoogle Scholar
[2]Meir, A. and Keeler, E., “A theorem on contraction mappings”, J. Math. Anal. Appl. 28 (1969), 326–329.CrossRefGoogle Scholar