`a`
Numerical Algebra, Control and Optimization (NACO)
 

Some new bounds for two mappings related to the Hermite-Hadamard inequality for convex functions
Pages: 271 - 278, Issue 2, June 2012

doi:10.3934/naco.2012.2.271      Abstract        References        Full text (125.9K)                  Related Articles

S. S. Dragomir - Mathematics, School of Engineering & Science, Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia (email)
I. Gomm - Mathematics, School of Engineering & Science, Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia (email)

1 A. G. Azpeitia, Convex functions and the Hadamard inequality, Rev. Colombiana Mat., 28 (1994), 7-12.
2 S. S. Dragomir, A mapping in connection to Hadamard's inequalities, An. Öster. Akad. Wiss. Math. Natur., (Wien), 128 (1991), 17-20.       
3 S. S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49-56.       
4 S. S. Dragomir, On Hadamard's inequalities for convex functions, Mat. Balkanica, 6 (1992), 215-222.       
5 S. S. Dragomir, An inequality improving the second Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products, J. Inequal. Pure & Appl. Math., 3 (2002), Art. 35. Available from: http://www.emis.de/journals/JIPAM/article187.html?sid=187
6 S. S. Dragomir, Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc., 74 (2006), 471-476.       
7 S. S. Dragomir and I. Gomm, Bounds for two mappings associated to the Hermite-Hadamard inequality, Aust. J. Math. Anal. Appl., 8 (2011), 9 pages.       
8 S. S. Dragomir, D. S. Milośević and J. Sándor, On some refinements of Hadamard's inequalities and applications, Univ. Belgrad, Publ. Elek. Fak. Sci. Math., 4 (1993), 21-24.
9 S. S. Dragomir and C. E. M. Pearce, "Selected Topics on Hermite-Hadamard Inequalities and Applications," RGMIA Monographs, 2000. Available from: http://rgmia.org/monographs/hermite_hadamard.html
10 A. Guessab and G. Schmeisser, Sharp integral inequalities of the Hermite-Hadamard type, J. Approx. Theory, 115 (2002), 260-288.       
11 E. Kikianty and S. S. Dragomir, Hermite-Hadamard's inequality and the p-HH-norm on the Cartesian product of two copies of a normed space, Math. Inequal. Appl., 13 (2010), 1-32.       
12 M. Merkle, Remarks on Ostrowski's and Hadamard's inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 10 (1999), 113-117.       
13 C. E. M. Pearce and A. M. Rubinov, P-functions, quasi-convex functions, and Hadamard type inequalities, J. Math. Anal. Appl., 240 (1999), 92-104.       
14 J. Pečarić and A. Vukelić, "Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions," Functional Equations, Inequalities and Applications, Kluwer Acad. Publ., Dordrecht, (2003), 105-137.
15 G. Toader, Superadditivity and Hermite-Hadamard's inequalities, Studia Univ. Babeş-Bolyai Math., 39 (1994), 27-32.       
16 G. S. Yang and M. C. Hong, A note on Hadamard's inequality, Tamkang J. Math., 28 (1997), 33-37.       
17 G. S. Yang and K. L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180-187.       

Go to top