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Schur-convex functions related to Hadamard-type inequalities. (English) Zbl 1131.26017
Summary: The Schur-convexity on the upper and the lower limit of the integral for a mean of the convex function is researched. As applications, a generalized logarithmic mean with a parameter is obtained and a relevant double inequality that is an extension of the known inequality is established.

MSC:
26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations
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