Abstract
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.
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Mayer, G. Epsilon-inflation with contractive interval functions. Applications of Mathematics 43, 241–254 (1998). https://doi.org/10.1023/A:1023297204431
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DOI: https://doi.org/10.1023/A:1023297204431