SOME NEW BONNESEN-STYLE INEQUALITIES
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By evaluating the containment measure of one domain to contain another, we will derive some new Bonnesen-type inequalities (Theorem 2) via the method of integral geometry. We obtain Ren's suf-cient condition for one domain to contain another domain (Theorem 4). We also obtain some new geometric inequalities. Finally we give a simplied proof of the Bottema's result.
Abstract
By evaluating the containment measure of one domain to contain another, we will derive some new Bonnesen-type inequalities (Theorem 2) via the method of integral geometry. We obtain Ren's suf-cient condition for one domain to contain another domain (Theorem 4). We also obtain some new geometric inequalities. Finally we give a simplied proof of the Bottema's result.
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