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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2038599
Page Count: 4
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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.
Proceedings of the American Mathematical Society © 1971 American Mathematical Society