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Numerical Algebra, Control and Optimization (NACO)
 

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

Pages: 1 - 8, Volume 4, Issue 1, March 2014      doi:10.3934/naco.2014.4.1

 
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Shu-Lin Lyu - Department of Mathematics, University of Macau, Macau, China (email)

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.

Keywords:  Hermite--Hadamard inequality, convex function, $p$-logarithmic mean, matrix function.
Mathematics Subject Classification:  Primary: 26D15, 26B25, 26E60; Secondary: 65F60.

Received: December 2012;      Revised: October 2013;      Available Online: December 2013.

 References