On the Hermite--Hadamard inequality for  convex functions of two variables

Shu-Lin  Lyu

doi:10.3934/naco.2014.4.1

Article Contents

2014, Volume 4, Issue 1: 1-8. Doi: 10.3934/naco.2014.4.1

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On the Hermite--Hadamard inequality for convex functions of two variables

Shu-Lin Lyu^1,

1.
Department of Mathematics, University of Macau, Macau

Received: November 30, 2012

Revised: September 30, 2013

Published: November 2013

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Abstract

Inspired by the results in [S. S. Dragomir and I. Gomm, Num. Alg. Cont. $\&$ Opt., 2 (2012), 271--278], we give some new bounds for two mappings related to the Hermite--Hadamard inequality for convex functions of two variables, and apply them to special functions to get some results for the $p$-logarithmic mean. We also apply the Hermite--Hadamard inequality to matrix functions in this paper.

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Mathematics Subject Classification: Primary: 26D15, 26B25, 26E60; Secondary: 65F60.

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