Roots of continuous piecewise monotone maps of an interval.
Blokh, A., Coven, E., Misiurewicz, Michał, Nitecki, Zbigniew (1991)
Acta Mathematica Universitatis Comenianae. New Series
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Blokh, A., Coven, E., Misiurewicz, Michał, Nitecki, Zbigniew (1991)
Acta Mathematica Universitatis Comenianae. New Series
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Alsedà, Ll., Mañosas, F. (1996)
Acta Mathematica Universitatis Comenianae. New Series
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De la Sen, M. (2010)
Fixed Point Theory and Applications [electronic only]
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L. Reich, Jaroslav Smítal, M. Štefánková (2004)
Mathematica Bohemica
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We consider the functional equation where is a given increasing homeomorphism of an open interval and is an unknown continuous function. In a series of papers by P. Kahlig and J. Smítal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under and which contains in its interior no fixed point except for . They also provide a characterization of the class of monotone solutions and prove a necessary and sufficient condition for...
Fotiades, Nikos A., Boudourides, Moses A. (2001)
International Journal of Mathematics and Mathematical Sciences
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Shultz, Fred (2005)
The New York Journal of Mathematics [electronic only]
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Agarwal, Ravi P., O'Regan, Donal (2001)
Journal of Applied Mathematics and Stochastic Analysis
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Dariusz Zagrodny (2010)
Czechoslovak Mathematical Journal
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It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator can be approximated by a sequence of maximal monotone operators of type NI, which converge to in a reasonable sense (in the sense of Kuratowski-Painleve convergence).