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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 simpli ed 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 simpli ed proof of the Bottema's result.

참고문헌 (48)

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