Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2018: 0.29

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 68, Issue 5

Issues

Generalization of Ostrowski inequality for convex functions

Silvestru Sever Dragomir
  • Mathematics, School of Engineering & Science, Victoria University, PO Box 14428, Melbourne City MC 8001, Australia
  • DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences School of Computer Science & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0164

Abstract

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.

MSC 2010: Primary 26D15; Secondary 26D20

Keywords: convex functions; integral inequalities; Jensen’s type inequalities; Fejér’s type inequalities; Lebesgue integral; midpoint type inequalities; special means

References

  • [1]

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

  • [4]

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

  • [5]

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

  • [8]

    DRAGOMIR, S. S.—PEARCE, C. E. M.: Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, 2000. Online: http://rgmia.org/monographs/hermite_hadamard.htmlGoogle Scholar

  • [9]

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

  • [10]

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

  • [12]

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

  • [13]

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

  • [16]

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

  • [17]

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

About the article

Received: 2017-04-21

Accepted: 2017-07-31

Published Online: 2018-10-20

Published in Print: 2018-10-25


Communicated by L’ubica Holá


Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1017–1040, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0164.

Export Citation

© 2018 Mathematical Institute Slovak Academy of Sciences.Get Permission

Comments (0)

Please log in or register to comment.
Log in