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Generalization of Ostrowski inequality for convex functions

Silvestru Sever Dragomir
From the journal Mathematica Slovaca


In this paper we establish some related Ostrowski inequalities for the case of convex functions and general Lebesgue integral on measurable spaces. Midpoint and integral mean inequalities are provided, some particular results related to the famous Fejér’s inequality are also given.


The author would like to thank the anonymous referee for valuable suggestions that have been implemented in the final version of the paper.

  1. Communicated by L’ubica Holá


[1] AZPEITIA, A. G.: Convex functions and the Hadamard inequality, Rev. Colombiana Mat. 28(1) (1994), 7–12.Search in Google Scholar

[2] DRAGOMIR, S. S.: A mapping in connection to Hadamard’s inequalities, An. Öster. Akad. Wiss. Math.-Natur. (Wien), 128 (1991), 17–20. MR 934:26032. ZBL No. 747:26015.Search in Google Scholar

[3] DRAGOMIR, S. S.: Two mappings in connection to Hadamard’s inequalities, J. Math. Anal. Appl. 167 (1992), 49–56. MR:934:26038, ZBL No. 758:26014.Search in Google Scholar

[4] DRAGOMIR, S. S.: On Hadamard’s inequalities for convex functions, Mat. Balkanica 6 (1992), 215–222. MR: 934:26033.Search in Google Scholar

[5] DRAGOMIR, S. S., Bounds for the normalized Jensen functional, Bull. Austral. Math. Soc. 74(3) (2006), 471–476.Search in Google Scholar

[6] DRAGOMIR, S. S.: Jensen and Ostrowski type inequalities for general Lebesgue integral with applications, Ann. Univ. Mariae Curie-Skodowska Sect. A 70(2) (2016), 29–49.Search in Google Scholar

[7] DRAGOMIR, S. S.—MILOŚEVIĆ, D. S.—SÁNDOR, J.: On some refinements of Hadamard’s inequalities and applications, Univ. Belgrad, Publ. Elek. Fak. Sci. Math. 4 (1993) 21–24.Search in Google Scholar

[8] DRAGOMIR, S. S.—PEARCE, C. E. M.: Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, 2000. Online: in Google Scholar

[9] FÉJER, L.: Über die Fourierreihen, II, Math. Naturwiss, Anz. Ungar. Akad. Wiss. 24 (1906) (in Hungarian), 369–390.Search in Google Scholar

[10] GUESSAB, A.—SCHMEISSER, G.: Sharp integral inequalities of the Hermite-Hadamard type, J. Approx. Theory 115 (2) (2002), 260–288.Search in Google Scholar

[11] KILIANTY, E.—DRAGOMIR, S. S.: Hermite-Hadamard’s inequality and the p-HH-norm on the Cartesian product of two copies of a normed space, Math. Inequal. Appl. 13 (1) (2010), 1–32.Search in Google Scholar

[12] MERKLE, M.: Remarks on Ostrowski’s and Hadamard’s inequality, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 10 (1999), 113–117.Search in Google Scholar

[13] OSTROWSKI, A.: Über die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert, Comment. Math. Hel 10 (1938), 226–227.Search in Google Scholar

[14] PEARCE, C. E. M.—RUBINOV, A. M.: P-functions, quasi-convex functions, and Hadamard type inequalities, J. Math. Anal. Appl. 240(1) (1999), 92–104.Search in Google Scholar

[15] PEČARIĆ, J.—VUKELIĆ, A.: Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions. In: Functional equations, inequalities and applications, Kluwer Acad. Publ., Dordrecht, 2003, pp. 105–137.Search in Google Scholar

[16] TOADER, G.: Superadditivity and Hermite-Hadamard’s inequalities, Stud. Univ. Babeş-Bolyai Math. 39(2) (1994), 27–32.Search in Google Scholar

[17] YANG, G.-S.—HONG, M.-C.: A note on Hadamard’s inequality, Tamkang J. Math. 28(1) (1997), 33–37.Search in Google Scholar

[18] YANG, G.-S.—TSENG, K.-L.: On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl. 239(1) (1999), 180–187.Search in Google Scholar

Received: 2017-04-21
Accepted: 2017-07-31
Published Online: 2018-10-20
Published in Print: 2018-10-25

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