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Proceedings of the American Mathematical Society

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

 

 

Fixed points of several classes of nonlinear mappings in Banach space


Author: Peter K. F. Kuhfittig
Journal: Proc. Amer. Math. Soc. 44 (1974), 300-306
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1974-0346607-6
MathSciNet review: 0346607
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Abstract: In the first part of the paper conditions for the existence of ordinary and higher order fixed points of individual and commutative families of nonlinear operators are obtained.

The second part deals with the existence of fixed points of an operator $ T:C \to X$ whose graph is closed in the Cartesian product topology induced by the strong topology in $ C$ and the weak topology in $ X$.

The convergence to fixed points of sequences of successive approximations is considered in both parts.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0346607-6
Keywords: Nonexpansive mappings, fixed points
Article copyright: © Copyright 1974 American Mathematical Society