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A Fixed Point Theorem for Semigroups of Mappings with a Contractive Iterate

V. M. Sehgal and J. W. Thomas
Proceedings of the American Mathematical Society
Vol. 29, No. 3 (Aug., 1971), pp. 565-568
DOI: 10.2307/2038599
Stable URL: http://www.jstor.org/stable/2038599
Page Count: 4
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Fixed Point Theorem for Semigroups of Mappings with a Contractive Iterate
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Abstract

In a recent paper, Felix E. Browder discussed continuous self-mappings on a metric space, satisfying a functional inequality. Browder gave sufficient conditions such that the successive approximations of any point for such mappings converge to a unique fixed point. In the present paper, Browder's result is extended to a commutative semigroup of mappings and also to single mappings that are not necessarily continuous and satisfy a weaker form of the functional inequality.

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