Geodesic
Fixed Point Theorems of the Banach and Krasnosel’skii Type for Mappings on $m$-tuple Cartesian Product of Banach Algebras and Systems of Generalized Gripenberg’s Equations
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 2, pp. 27-39.

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In this paper we prove some fixed point theorems of the Banach and Krasnosel’skii type for mappings on the $m$-tuple Cartesian product of a Banach algebra $X$ over $\mathbb {R}$. Using these theorems existence results for a system of integral equations of the Gripenberg’s type are proved. A sufficient condition for the nonexistence of blowing-up solutions of this system of integral equations is also proved.
Classification : 45G15, 47B48, 47H10, 92D30
Keywords: fixed point; Banach algebra; integral equation; integro-differential system; epidemic model; blowing-up solution 
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Brestovanská, Eva; Medveď, Milan. Fixed Point Theorems of the Banach and Krasnosel’skii Type for Mappings on $m$-tuple Cartesian Product of Banach Algebras and Systems of Generalized Gripenberg’s Equations. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 2, pp. 27-39. http://geodesic.mathdoc.fr/item/AUPO_2012__51_2_a2/