Publ. Math. Debrecen  78/2 (2011), 393-403
DOI: 10.5486/PMD.2011.4777

Two Schur-convex functions related to Hadamard-type integral inequalities

By HUAN-NAN SHI (Beijing)

Abstract. The Schur-convexity, the Schur-geometric convexity and the Schur-harmonic convexity of two mappings which related to Hadamard-type integral inequalities are researched. And three re¯nements of Hadamard-type integral inequality are obtained, as applications, some inequalities related to the arithmetic mean, the loga-rithmic mean and the power mean are established.

Mathematics Subject Classification: Primary: 26D15, 26A51; Secondary: B25, 26D15.

Key words and phrases: Schur-convex function, Schur-geometrical convex function and the
Schur-harmonic convex function,inequality, convex function Hadamard's inequality; logarith-
mic mean, power mean.

4777-Shi.pdf

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