Epsilon-inflation with contractive interval functions
Günter Mayer · Applications of Mathematics · 1998
For contractive interval functions [g] we show that $$[g]([x]_\varepsilon ^{k_0 } ) \subseteq \operatorname{int} ([x]_\varepsilon ^{k_0 } )$$ results from the iterative process $$[x]^{k + 1} : = [g]([x]_\varepsilon ^k )$$ after finitely many iterations if one uses the epsilon-inflated vector $$[x]_\varepsilon ^k$$ as input for [g] instead of the original output vector [x] k . Applying Brouwer's fixed point theorem, zeros of various mathematical problems can be verified in this way.