A fixed point theorem for semi-groups of mappings with a contractive iterate
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- by V. M. Sehgal and J. W. Thomas PDF
- Proc. Amer. Math. Soc. 29 (1971), 565-568 Request permission
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.References
- D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458–464. MR 239559, DOI 10.1090/S0002-9939-1969-0239559-9
- Felix E. Browder, On the convergence of successive approximations for nonlinear functional equations, Nederl. Akad. Wetensch. Proc. Ser. A 71=Indag. Math. 30 (1968), 27–35. MR 0230180, DOI 10.1016/S1385-7258(68)50004-0
- L. F. Guseman Jr., Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc. 26 (1970), 615–618. MR 266010, DOI 10.1090/S0002-9939-1970-0266010-3
- V. M. Sehgal, A fixed point theorem for mappings with a contractive iterate, Proc. Amer. Math. Soc. 23 (1969), 631–634. MR 250292, DOI 10.1090/S0002-9939-1969-0250292-X
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 565-568
- MSC: Primary 47.85; Secondary 54.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0282277-0
- MathSciNet review: 0282277