# American Institute of Mathematical Sciences

2014, 4(1): 1-8. doi: 10.3934/naco.2014.4.1

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

 1 Department of Mathematics, University of Macau, Macau, China

Received  December 2012 Revised  October 2013 Published  December 2013

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.
Citation: Shu-Lin Lyu. On the Hermite--Hadamard inequality for convex functions of two variables. Numerical Algebra, Control & Optimization, 2014, 4 (1) : 1-8. doi: 10.3934/naco.2014.4.1
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