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Ky Fan’s inequality via convexity. (English) Zbl 1163.26340

Summary: Using the strict convexity and concavity of the function \( f(x)=\frac{1}{1+e^x}\) on \( [0,\infty)\) and \( (-\infty,0]\) respectively, we prove Ky Fan’s inequality by separating the left and right hands of it by \( \frac{1}{G_n+G^{\prime }_n}\).

MSC:

26D15 Inequalities for sums, series and integrals
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