Geodesic
Continuous evolution of equations and inclusions involving set-valued contraction mappings with applications to generalized fractal transforms
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let T be a set-valued contraction mapping on a general Banach space $\mathcal{B}$. In the first part of this paper we introduce the evolution inclusion $\dot x + x \in Tx$ and study the convergence of solutions to this inclusion toward fixed points of T. Two cases are examined: (i) T has a fixed point $\bar y \in \mathcal{B}$ in the usual sense, i.e., $\bar y = T \bar y$ and (ii) T has a fixed point in the sense of inclusions, i.e., $\bar y \in T \bar y$. In the second part we extend this analysis to the case of set-valued evolution equations taking the form $\dot x + x = Tx$. We also provide some applications to generalized fractal transforms.
Classification : 34A60, 28A80
Keywords: set-valued evolution inclusions, set-valued evolution equations, contractive set-valued functions, fixed points 
@article{EJDE_2014__2014__a52,
     author = {Kunze, Herb and La Torre, Davide and Mendivil, Franklin and Vrscay, Edward R.},
     title = {Continuous evolution of equations and inclusions involving set-valued contraction mappings with applications to generalized fractal transforms},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a52/}
}
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Kunze, Herb; La Torre, Davide; Mendivil, Franklin; Vrscay, Edward R. Continuous evolution of equations and inclusions involving set-valued contraction mappings with applications to generalized fractal transforms. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a52/