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On subsequential limit points of a sequence of iterates. II

Part of: Nonlinear operators and their properties Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

M. Maiti  and
A. C. Babu
M. Maiti
Affiliation:
Department of Mathematics Indian Institue of Technology Kharagpur, 721302, India
A. C. Babu
Affiliation:
Department of Mathematics University College of Engineering Burla, 768018, India
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Abstract

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J. B. Diaz and F. T. Metcalf established some results concerning the structure of the set of cluster points of a sequence of iterates of a continuous self-map of a metric space. In this paper it is shown that their conclusions remain valid if the distance function in their inequality is replaced by a continuous function on the product space. Then this idea is extended to some other mappings and to uniform and general topological spaces.

MSC classification

Secondary: 47H10: Fixed-point theorems 54H25: Fixed-point and coincidence theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 1 , February 1985 , pp. 118 - 129
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Berge, C., Topological spaces (Oliver and Boyd, 1963).Google Scholar
[2]Browder, F. E. and Petryshyn, W. V., ‘The solution by iteration of linear functional equations in Banach spaces’, Bull. Amer. Math. Soc. 72 (1966), 566–570.CrossRefGoogle Scholar
[3]Browder, F. E. and Petryshyn, W. V., ‘The solution by iteration of nonlinear functional equations in Banach spaces’, Bull. Amer. Math. Soc. 72 (1966), 571–575.Google Scholar
[4]Caristi, J., ‘Fixed point theorems for mappings satisfying inwardness conditions’, Trans. Amer. Math. Soc. 215 (1976), 241–251.Google Scholar
[5]Diaz, J. B. and Metcalf, F. T., ‘On the structure of the set of subsequential limit points of successive approximations’, Bull. Amer. Math. Soc. 73 (1967), 516–519.CrossRefGoogle Scholar
[6]Diaz, J. B. and Metcalf, F. T., ‘On the structure of the set of subsequential limit points of successive approximations’, Trans. Amer. Math. Soc. 135 (1969), 459–485.Google Scholar
[7]Dotson, W. G. Jr, ‘On the Mann iterative process’, Trans. Amer. Math. Soc. 149 (1970), 65–73.CrossRefGoogle Scholar
[8]Maiti, M. and Babu, A. C., ‘On sebsequential limit points of a sequence of iterates’, Proc. Amer. Math. Soc. 82 (1981), 377–381.Google Scholar
[9]Singh, S. P. and Zorzitto, F., ‘On fixed point theorems in metric spaces’, Ann. Soc. Sci. Bruxelles 85 (1971), 117–123.Google Scholar
[10]Tarafdar, E., ‘An approach to fixed point theorems on uniform spaces’, Trans. Amer. Math. Soc. 191 (1974), 209–225.CrossRefGoogle Scholar
[11]Thron, W. J., Topological structures (Holt, Rinehart and Winston, New York, 1966).Google Scholar