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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A fixed point theorem for semi-groups of mappings with a contractive iterate


Authors: V. M. Sehgal and J. W. Thomas
Journal: Proc. Amer. Math. Soc. 29 (1971), 565-568
MSC: Primary 47.85; Secondary 54.00
MathSciNet review: 0282277
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0282277-0
Keywords: Pointwise contractive semigroup
Article copyright: © Copyright 1971 American Mathematical Society