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

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