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Proceedings of the American Mathematical Society

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


Author: S. Venkateswaran
Journal: Proc. Amer. Math. Soc. 36 (1972), 313-314
MSC: Primary 47H15
DOI: https://doi.org/10.1090/S0002-9939-1972-0308885-7
MathSciNet review: 0308885
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Abstract: It is proved that if f is a continuous nonlinear operator on a Banach space E then $ f(x) = kx$ has a solution when $ \vert k\vert$ is sufficiently large.


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

  • [1] Robert A. Bonic, Linear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York-London-Paris, 1969. MR 0257686

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0308885-7
Keywords: Banach space, nonlinear operator, fixed point theorem
Article copyright: © Copyright 1972 American Mathematical Society