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Re: Probleme ouvert dans la theorie du point fixe

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sadf...@gmail.com

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Dec 7, 2016, 8:45:42 AM12/7/16
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On Tuesday, December 5, 2006 3:02:00 PM UTC + 1, wrote math:
> Probleme ouvert
>
> Le theoreme du point fixe de Kannan suggere le probleme suivant:
>
> Soit (E,I.I) un espace de Banach.D est un sous-ensemble de E,
>
> ferme, borne et convexe.T est une application continue de D dans D,
>
> verifiant la 'contraction' suivante:
>
>       ITx-TyI\leq max[Ix-TxI,Iy-TyI],  sur DxD
>
>  T admet-t'elle un point fixe si E est un 'bon' espace,
>
> par exemple, les espaces:de Hilbert,uniformement convexes,
>
> à structure normale,uniformement localement convexes.?
>
>                            Mes salutations
>
>                            Hanebaly,E.(Rabat)


salut Monsieur je vous demande si ce probléme est encore ouvert ou non
cordialement

**Translations**

> Open Problem
>
> The Kannan fixed point theorem suggests the following problem:
>
> Let (E, \|.\|) be a Banach space. Let D be a closed, convex, bounded
> subset of E. Let T be a continuous function from D to D verifying
> the following 'contraction' property:
>
> \| Tx - Ty \| \leq \max [ \| x - Tx \| , \| y - Ty \| ] on D x D
>
> Then must T have a fixed point if E is a 'good' space: for example,
> Hilbert space, uniformly convex, with normal structure, locally
> uniformly convex?

Greetings, Sir. I ask whether or not this problem is still open.
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