On the Hermite-Hadamard inequality and other integral inequalities involving two functions. (English) Zbl 1194.26037

Summary: We establish some new Hermite-Hadamard-type inequalities involving product of two functions. Other integral inequalities for two functions are obtained as well. The analysis used in the proofs is fairly elementary and based on the use of the Minkowski, Hölder, and Young inequalities.


26D15 Inequalities for sums, series and integrals
Full Text: DOI EuDML


[1] Pachpatte, BG, On some inequalities for convex functions, No. 6, (2003)
[2] Pachpatte, BG, A note on integral inequalities involving two log-convex functions, Mathematical Inequalities & Applications, 7, 511-515, (2004) · Zbl 1073.26016
[3] Bakula, MK; Özdemir, ME; Pečarić, J, Hadamard type inequalities for -convex and -convex functions, (2008)
[4] Kirmaci, US; Bakula, MK; Özdemir, ME; Pečarić, J, Hadamard-type inequalities for [inlineequation not available: see fulltext.]-convex functions, Applied Mathematics and Computation, 193, 26-35, (2007) · Zbl 1193.26020
[5] Bakula, MK; Pečarić, J; Ribičić, M, Companion inequalities to Jensen’s inequality for -convex and -convex functions, (2006) · Zbl 1130.26005
[6] Bakula, MK; Pečarić, J, Note on some Hadamard-type inequalities, (2004) · Zbl 1055.26017
[7] Dragomir, SS; Agarwal, RP; Barnett, NS, Inequalities for beta and gamma functions via some classical and new integral inequalities, Journal of Inequalities and Applications, 5, 103-165, (2000) · Zbl 0948.26011
[8] Hardy GH, Littlewood JE, Pólya G: Inequalities. Cambridge Mathematical Library, Cambridge , UK; 1998:xii+324. · Zbl 0634.26008
[9] Kirmaci, US; Özdemir, ME, Some inequalities for mappings whose derivatives are bounded and applications to special means of real numbers, Applied Mathematics Letters, 17, 641-645, (2004) · Zbl 1057.26018
[10] Mitrinović DS, Pečarić JE, Fink AM: Classical and New Inequalities in Analysis, Mathematics and Its Applications (East European Series). Volume 61. Kluwer Academic Publishers, Dordrecht, The Netherlands; 1993:xviii+740. · Zbl 0771.26009
[11] Özdemir, ME; Kırmacı, US, Two new theorem on mappings uniformly continuous and convex with applications to quadrature rules and means, Applied Mathematics and Computation, 143, 269-274, (2003) · Zbl 1020.26012
[12] Pachpatte BG: Inequalities for Differentiable and Integral Equations. Academic Press, Boston, Mass, USA; 1997.
[13] Pečarić, J; Pejković, T, On an integral inequality, (2004) · Zbl 1066.26022
[14] Pečarić JE, Proschan F, Tong YL: Convex Functions, Partial Orderings, and Statistical Applications, Mathematics in Science and Engineering. Volume 187. Academic Press, Boston, Mass, USA; 1992:xiv+467. · Zbl 0749.26004
[15] Pogány, TK, On an open problem of F. qi, (2002) · Zbl 1096.26504
[16] Bullen PS, Mitrinović DS, Vasić PM: Means and Their Inequalities, Mathematics and Its Applications (East European Series). Volume 31. D. Reidel, Dordrecht, The Netherlands; 1988:xx+459.
[17] Kirmaci, US; Klaričić, M; Özdemir, ME; Pečarić, J, On some inequalities for -norms, (2008) · Zbl 1163.26333
[18] Bougoffa, L, On Minkowski and Hardy integral inequalities, (2006) · Zbl 1132.26007
[19] Alomari, M; Darus, M, On the Hadamard’s inequality for log-convex functions on the coordinates, No. 2009, 13, (2009) · Zbl 1175.26032
[20] Dinu, C, Hermite-Hadamard inequality on time scales, No. 2008, 24, (2008) · Zbl 1151.26320
[21] Dragomir SS, Pearce CEM: Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University, Melbourne, Australia; 2000.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.