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)
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},
     year = {2014},
     volume = {2014},
     zbl = {1329.34106},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a52/}
}
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JO  - Electronic journal of differential equations
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%A Vrscay,  Edward R.
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%J Electronic journal of differential equations
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%F EJDE_2014__2014__a52
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/