Geodesic
On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces
Commentationes Mathematicae, Tome 51 (2011) no. 1, pp. 81-98.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Let \(C\) be a \(\rho\)-bounded, \(\rho\)-closed, convex subset of a modular function space \(L_\rho\). We investigate the existence of common fixed points for semigroups of nonlinear mappings \(T_t\colon C\to C\), i.e. a family such that \(T_0(x) = x\), \(T_{s+t} = T_s (T_t (x))\), where each \(T_t\) is either \(\rho\)-contraction or \(\rho\)-nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.
DOI : 10.14708/cm.v51i1.5311
Mots-clés : Fixed point, common fixed point, nonexpansive mapping, contractions, semigroup of mappings, modular function space, modular space, Orlicz space, Musielak-Orlicz space 
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Wojciech M. Kozlowski. On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces. Commentationes Mathematicae, Tome 51 (2011) no. 1, pp.  81-98. doi : 10.14708/cm.v51i1.5311. http://geodesic.mathdoc.fr/articles/10.14708/cm.v51i1.5311/

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