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Variation on Shapiro's

Source: Kürschák 1986, problem 2

July 27, 2014
inequalitiesinequalities unsolved

Problem Statement

Let n>2n>2 be a positive integer. Find the largest value hh and the smallest value HH for which h<a1a1+a2+a2a2+a3+⋯+anan+a1<Hh<{a_1\over a_1+a_2}+{a_2\over a_2+a_3}+\cdots+{a_n\over a_n+a_1}<H holds for any positive reals a1,…,ana_1,\dots,a_n.
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