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A note on the solution of a class of functional equations. (English) Zbl 0604.39006
Let X and Y be Banach spaces, $S\subseteq X$ and $D\subseteq Y$. Let T:S$\times D\to S$, g:S$\times D\to R$, G:S$\times D\times R\to R$ and f:S$\to R$ be maps where R is the field of real numbers. The authors provide two sets of sufficient conditions so that the equation $f(x)=\sup\sb{y\in D}\vert g(x,y)+G(x,y,f(T(x,y))\vert,$ $x\in S$ has a unique solution. The proofs are based on a fixed point theorem for non- self maps analogous to that of Browder’s theorem.
Reviewer: H.L.Vasudeva

39B52Functional equations for functions with more general domains and/or ranges
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
90C39Dynamic programming
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