Displaying similar documents to “On uniqueness of conjugacy of continuous and piecewise monotone functions.”

The continuous solutions of a generalized Dhombres functional equation

L. Reich, Jaroslav Smítal, M. Štefánková (2004)

Mathematica Bohemica

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We consider the functional equation f ( x f ( x ) ) = ϕ ( f ( x ) ) where ϕ J → J is a given increasing homeomorphism of an open interval J ⊂ ( 0 , ∞ ) and f ( 0 , ∞ ) → J 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 ϕ and which contains in its interior no fixed point except for 1 . They also provide a characterization of the class of monotone solutions and prove a necessary and sufficient condition for...

On maximal monotone operators with relatively compact range

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 T can be approximated by a sequence of maximal monotone operators of type NI, which converge to T in a reasonable sense (in the sense of Kuratowski-Painleve convergence).