Abstract. It is proved that --- under certain conditions --- continuous solutions $f$ of the functional equation $$ f(x)=h(x,y,f(g_1(x,y)),\ldots,f(g_n(x,y))), (x,y)\in D\subset{{\msbm R}^s}\times{\msbm R}^l, $$ are ${{\cal C}^\infty }$, even if $1\le l\le s$. As a tool we introduce new function classes which --- roughly speeking --- interpolate between differentiable and continuous functions.
AMS Subject Classification
(1991): 39B05, 26B05
Received October 27, 2000. (Registered under 2813/2009.)
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