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An equation $ f(x)=kx$ possessing no solutions


Authors: K. Goebel and Witold Rzymowski
Journal: Proc. Amer. Math. Soc. 51 (1975), 322
MSC: Primary 47H15
DOI: https://doi.org/10.1090/S0002-9939-1975-0372698-3
MathSciNet review: 0372698
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Abstract: An example is given of a nonlinear operation $ f:C[0,1] \to C[0,1]$ having for any $ k \in R$ no solutions of the equation $ f(x) = kx$.


References [Enhancements On Off] (What's this?)

  • [1] S. Venkateswaran, The existence of a solution of $ f(x) = kx$ for a continuous not necessarily linear operator, Proc. Amer. Math. Soc. 36 (1972), 313-314. MR 46 #7997. MR 0308885 (46:7997)

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DOI: https://doi.org/10.1090/S0002-9939-1975-0372698-3
Article copyright: © Copyright 1975 American Mathematical Society

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