Abstract
Recently some new Hermite-Hadamard-type inequalities for convex functions are established by Tseng et al. [Computers and Mathematics with Applications, 62, 401-418, 2011]. In this paper, we give some generalizations of this result.
Similar content being viewed by others
References
P. Czinder and Z. Pâles, An extension of the Hermite-Hadamard inequality and an application for Gini and Stolarsky means, J. Inequal. Pure Appl. Math., 5 (2004) 2.Art. 42; Available online at http://www.emis.de/journals/JIPAM/article399. html?sid=399.
S. S. Dragomir, Two mappings in connection to Hadamard's inequalities, J. Math. Anal. Appl., 167 (1992), 49–56.
S. S. Dragomir, A refinement of Hadamard's inequality for isotonic linear functionals, Tamkang. J. Math., 24 (1993), 101–106.
S. S. Dragomir, D. S. Milosevic and Jözsef Sâ ndor, On some refinements of Hadamard's inequalities and applications, Univ. Belgrad. Puhl. Elek. Fak. Sei. Math., 4 (1993), 3–10.
S. S. Dragomir, On the Hadamard's inequality for convex on the co-ordinates in a rectangle from the plane, Taiwanese J. Math., 5(4) (2001), 775–788.
S. S. Dragomir, Further proprtities of some mapping associoateed with Hermite-Hadamard inequalities, Tamkang. J. Math., 34(1) (2003), 45–57.
S. S. Dragomir, Y.-J. Cho and S.-S. Kim, Inequalities of Hadamards type for Lipschitzian mappings and their applications, J. Math. Anal. Appl, 245 (2000), 489–501.
S. S. Dragomir, Hermite-Hadamard's type inequalities for operator convex functions, Appl. Math. Comput., doi:10.1016/j.amc.2011.01.056.
L. Fejér, ber die Fourierreihen, II, Math. Naturwiss. Anz Ungar. Akad. Wiss., 24 (1906), 369–390, (In Hungarian). /
J. Hadamard, Etude sur les propriétés des fonctions entières en particulier d'une fonction considérée par Riemann, J. Math. Pures Appl., 58 (1893), 171–215.
D.-Y. Hwang, K.-L. Tseng and G.-S. Yang, Some Hadamard's inequalities for coordinated convex functions in a rectangle from the plane, Taiwanese J. Math., 11(1) (2007), 63–73.
A. Matkovic, J. Pecäric and I. Peric, A variant of Jensens inequality of Mercers type for operators with applications, Linear Algebra Appl, 418(2-3) (2006), 551–564.
B.G. Pachpatte, On some inequalities for convex functions, RGMIA Research Report Collection 6(E) (2003). Available online at http://rgmia.org/v6(E).php.
K.-L. Tseng, S.-R. Hwang and S. S. Dragomir, On some new inequalities of Hermite- Hadamard-Fejr type involving convex functions, Demonstratio Math., XL(1) (2007), 51–64.
K.-L. Tseng, G.-S. Yang and K.-C. Hsu, On some inequalities of Hadamards type and applications, Taiwanese J. Math., 13(6B) (2009), 1929–1948.
K.-L. Tseng, S.-R. Hwang and S. S. Dragomir, New Hermite-Hadamard-type inequalities for convex functions (II), Comput. Math. Appl, 62 (2011), 401–418.
K.-L. Tseng, S.-R. Hwang and S. S. Dragomir, New Hermite-Hadamard-type inequalities for convex functions (I), Applied Mathematics Letters, 25 (2012), 1005–1009.
Z.-G. Xiao, Z.-H. Zhang and Y.-D. Wu, On weighted Hermite-Hadamard inequalities, Appl. Math. Comput., doi:10.1016/j.amc.2011.03.081.
G.-S. Yang and M.-C. Hong, A note on Hadamards inequality, Tamkang. J. Math., 28(1) (1997), 33–37.
G.-S. Yang and K.-L. Tseng, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239 (1999), 180–187.
G.-S. Yang and K.-L. Tseng, Inequalities of Hadamard's Type for lipschitzian mappings, J. Math. Anal. Appl, 260 (2001), 230–238.
G.-S. Yang and K.-L. Tseng, On certain multiple integral inequalities related to Hermite- Hadamard inequalities, Utilitas Math., 62 (2002), 131–142.
G.-S. Yang and K.-L. Tseng, Inequalities of Hermite-Hadamard-Fejr type for convex functions and lipschitzian functions, Taiwanese J. Math., 7(3) (2003), 433–440.
Author information
Authors and Affiliations
Corresponding author
Additional information
The research of this author is partially supported by the grant MYRG2015-00064-FST from University of Macau and the Macao Science and Technology Development Fund (FDCT) 001/2013/A.
Rights and permissions
About this article
Cite this article
Fok, H., Vong, S. Generalizations of some Hermite-Hadamard-type inequalities. Indian J Pure Appl Math 46, 359–370 (2015). https://doi.org/10.1007/s13226-015-0121-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-015-0121-z