American Institute of Mathematical Sciences

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2012, 2(2): 271-278. doi: 10.3934/naco.2012.2.271

Some new bounds for two mappings related to the Hermite-Hadamard inequality for convex functions

S. S. Dragomir 1, and  I. Gomm 1,

1. 

Mathematics, School of Engineering & Science, Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia, Australia

Received  October 2011 Revised  March 2012 Published  May 2012

Some new results concerning two mappings associated to the celebrated Hermite-Hadamard integral inequality for convex function with applications for special means are given.
Keywords: Convex functions, special means., Hermite-Hadamard inequality.
Mathematics Subject Classification: Primary: 26D15; Secondary: 25D1.
Citation: S. S. Dragomir, I. Gomm. Some new bounds for two mappings related to the Hermite-Hadamard inequality for convex functions. Numerical Algebra, Control & Optimization, 2012, 2 (2) : 271-278. doi: 10.3934/naco.2012.2.271
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show all references

References:
[1]

Rev. Colombiana Mat., 28 (1994), 7-12. Google Scholar

[2]

An. Öster. Akad. Wiss. Math. Natur., (Wien), 128 (1991), 17-20.  Google Scholar

[3]

J. Math. Anal. Appl., 167 (1992), 49-56. doi: 10.1016/0022-247X(92)90233-4.  Google Scholar

[4]

Mat. Balkanica, 6 (1992), 215-222.  Google Scholar

[5]

J. Inequal. Pure & Appl. Math., 3 (2002), Art. 35. Available from: http://www.emis.de/journals/JIPAM/article187.html?sid=187 Google Scholar

[6]

Bull. Austral. Math. Soc., 74 (2006), 471-476. doi: 10.1017/S000497270004051X.  Google Scholar

[7]

Aust. J. Math. Anal. Appl., 8 (2011), 9 pages.  Google Scholar

[8]

Univ. Belgrad, Publ. Elek. Fak. Sci. Math., 4 (1993), 21-24. Google Scholar

[9]

RGMIA Monographs, 2000. Available from: http://rgmia.org/monographs/hermite_hadamard.html Google Scholar

[10]

J. Approx. Theory, 115 (2002), 260-288. doi: 10.1006/jath.2001.3658.  Google Scholar

[11]

Math. Inequal. Appl., 13 (2010), 1-32.  Google Scholar

[12]

Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 10 (1999), 113-117.  Google Scholar

[13]

J. Math. Anal. Appl., 240 (1999), 92-104. doi: 10.1006/jmaa.1999.6593.  Google Scholar

[14]

Functional Equations, Inequalities and Applications, Kluwer Acad. Publ., Dordrecht, (2003), 105-137. Google Scholar

[15]

Studia Univ. Babeş-Bolyai Math., 39 (1994), 27-32.  Google Scholar

[16]

Tamkang J. Math., 28 (1997), 33-37.  Google Scholar

[17]

J. Math. Anal. Appl., 239 (1999), 180-187. doi: 10.1006/jmaa.1999.6506.  Google Scholar

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