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Fixed points for discontinuous quasi-monotone maps in sequence spaces


Author: Sabina Schmidt
Journal: Proc. Amer. Math. Soc. 115 (1992), 361-363
MSC: Primary 47H10; Secondary 47H05
DOI: https://doi.org/10.1090/S0002-9939-1992-1081098-2
MathSciNet review: 1081098
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Abstract: In [2] Hu gives a fixed point theorem for discontinuous quasimonotone increasing maps in $ X = {\mathbb{R}^n}$. We will answer the question in [2] as to whether this result can be extended to $ X = {l^p},1 \leq p \leq \infty $.


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

  • [1] A. Chaljub-Simon and P. Volkmann, Un théorème d'existence et de comparison pour des équations différentielles dans les espaces de fonctions bornées, C.R. Acad. Sci. Paris Ser. I Math. (to appear).
  • [2] S.-C. Hu, Fixed points for discontinuous quasi-monotone maps in $ {\mathbb{R}^n}$, Proc. Amer. Math. Soc. 104 (1988), 1111-1114. MR 937846 (89k:47093)
  • [3] P. Volkmann, Gewöhnliche Differentialgleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen, Math. Z. 127 (1972), 157-164. MR 0308547 (46:7661)
  • [4] E. Zeidler, Nonlinear functional analysis and its applications, vol. I, Springer-Verlag, Berlin and New York, 1986. MR 816732 (87f:47083)

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DOI: https://doi.org/10.1090/S0002-9939-1992-1081098-2
Article copyright: © Copyright 1992 American Mathematical Society

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