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Keywords:
fixed point; Banach algebra; integral equation; integro-differential system; epidemic model; blowing-up solution
fixed point; Banach algebra; integral equation; integro-differential system; epidemic model; blowing-up solution
Summary:
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.
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