On the existence of a solution of $f(x)=kx$ for a continuous not necessarily linear operator
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- by Ana I. Istrăţescu and Vasile I. Istrăţescu PDF
- Proc. Amer. Math. Soc. 48 (1975), 197-198 Request permission
Abstract:
In a recent paper, S. Venkateswaran has asserted that $f(x) = kx$ has a solution when $|k|$ is sufficiently large. In the paper a counterexample to this assertion is given, and it is indicated when the assertion is true.References
- 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 308885, DOI 10.1090/S0002-9939-1972-0308885-7 S. Marteli and A. Vignoli, Eigenvectors and surjectivity for $\alpha$-Lipschitz mappings in Banach spaces, Ann. Mat. Pura Appl. (4) 94 (1972).
- V. Istrăţescu and A. Istrăţescu, On the theory of fixed points for some classes of mappings. I, Bull. Math. Soc. Sci. Math. R.S. Roumanie (N.S.) 14(62) (1970), no. 4, 419–426 (1972). MR 0358455
- Robert A. Bonic, Linear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York-London-Paris, 1969. MR 0257686
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 197-198
- MSC: Primary 47H15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0358473-4
- MathSciNet review: 0358473