Geodesic
About existence and estimation of solution to one integral inclusion
Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 6, pp. 1247-1254

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An inclusion with multi-valued mapping acting in spaces with vector-valued metrics is under discussion. It is shown that, if a multi-valued mapping $F$ can be written as $F(x)=\Upsilon(x,x),$ where the mapping $\Upsilon$ is closed and metrically regular with some operator coefficient $K$ with respect to one argument, Lipschitz with operator coefficient $Q$ with respect to the other argument, and the spectral radius of the operator $KQ$ is less than one, then the inclusion $F(x)\ni y$ is solvable. The estimations of the vector-valued distance from a solution $x$ of the inclusion to a given element $x_0$ are derived. In the second part of the paper, these results are used to investigate an integral inclusion of the implicit type with respect to the unknown integrable function.
Keywords: space with vector-valued metric, multi-valued mapping, metrically regular mapping, implicit type integral inclusion. 
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     author = {S. Benarab and W. Merchela and E. A. Panasenko},
     title = {About existence and estimation of solution to one integral inclusion},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {1247--1254},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2017_22_6_a3/}
}
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S. Benarab; W. Merchela; E. A. Panasenko. About existence and estimation of solution to one integral inclusion. Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 6, pp. 1247-1254. http://geodesic.mathdoc.fr/item/VTAMU_2017_22_6_a3/