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Proceedings of the American Mathematical Society

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On the existence of a solution of $ f(x)=kx$ for a continuous not necessarily linear operator


Authors: Ana I. Istrăţescu and Vasile I. Istrăţescu
Journal: Proc. Amer. Math. Soc. 48 (1975), 197-198
MSC: Primary 47H15
MathSciNet review: 0358473
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Abstract: In a recent paper, S. Venkateswaran has asserted that $ f(x) = kx$ has a solution when $ \vert k\vert$ is sufficiently large. In the paper a counterexample to this assertion is given, and it is indicated when the assertion is true.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0358473-4
Keywords: Continuous nonlinear operator, Altman fixed point theorem, condensing operator, densifying operator
Article copyright: © Copyright 1975 American Mathematical Society