Toufik Mansour and Mark Shattuck, Improving upon a geometric inequality of third order,
Forum Geometricorum, 12 (2012) 227--235.

Abstract.   We show that the best possible positive constant k in a certain geometric inequality of third order lies in the interval [0.14119,0.14364], which improves upon a previous known result where k=0. We also consider a comparable question concerning a fourth order version of the inequality.

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