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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show all references

References:
[1]

Int. J. Contemp. Math. Sci., 3 (2008), 1557-1567.  Google Scholar

[2]

Math. Pract. Theory, 25 (1995), 16-20. (Chinese) Google Scholar

[3]

Taiwanese J. Math., 5 (2001), 775-788.  Google Scholar

[4]

Num. Alg. Cont. & Opt., 2 (2012), 271-278. doi: 10.3934/naco.2012.2.271.  Google Scholar

[5]

RGMIA Monographs, Victoria University, 2000. Google Scholar

[6]

Computers. Math. Applic., 33 (1997), 15-20. doi: 10.1016/S0898-1221(97)00084-9.  Google Scholar

[7]

Appl. Math. Lett., 11 (1998), 105-109. doi: 10.1016/S0893-9659(97)00142-0.  Google Scholar

[8]

SIAM, 2008. doi: 10.1137/1.9780898717778.  Google Scholar

[9]

Taiwanese J. Math., 11 (2007), 63-73.  Google Scholar

[10]

Int. J. Math. Anal., 3 (2009), 1645-1656.  Google Scholar

[11]

J. Inequal. Appl., 1 (2012), 1-13. doi: 10.1186/1029-242X-2012-28.  Google Scholar

[12]

Hacet. J. Math. Stat., 40 (2011), 219-229.  Google Scholar

[13]

2nd edition, Higher Education Press, Beijing, 2006. (Chinese) Google Scholar

[14]

Princeton University Press, Princeton, 1951.  Google Scholar

[15]

Integr. Transf. Spec. F., 25 (2014), 134-147. doi: 10.1080/10652469.2013.824436.  Google Scholar

[16]

Tamsui Oxf. J. Inf. Math. Sci., 28 (2012), 137-152.  Google Scholar

[17]

Journal of Guyuan Teachers College (Natural Science Edition), 24 (2003), 27-30. (Chinese) Google Scholar

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