Aequationes mathematicae

, Volume 90, Issue 4, pp 705–718 | Cite as

On the Jensen functional and superquadraticity

  • Flavia-Corina Mitroi-Symeonidis
  • Nicuşor Minculete


In this note we give a recipe which describes upper and lower bounds for the Jensen functional under superquadraticity conditions. Some results involve the Chebychev functional. We give a more general definition of these functionals and establish analogous results.


Jensen functional Chebychev functional superquadratic function 

Mathematics Subject Classification

Primary 26B25 Secondary 26D15 


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  1. 1.
    Abramovich S., Dragomir S.S.: Normalized Jensen functional, superquadracity and related inequalities. Int. Ser. Numer. Math. 157, 217–228 (2009)MathSciNetMATHGoogle Scholar
  2. 2.
    Abramovich, S., Jameson, G., Sinnamon, G.: Refining Jensen’s inequality. Bull. Math. Soc. Sci. Math. Roum. (N.S.) 47(95), no. 1–2, 3–14 (2004)Google Scholar
  3. 3.
    Abramovich, S., Ivelić, S., Pečarić, J.: Refinement of inequalities related to convexity via superquadraticity, weaksuperquadraticity and superterzaticity. In: Inequalities and Applications 2010, pp. 191–207, International Series of Numerical Mathematics, 161. Birkhauser/Springer, Basel (2012)Google Scholar
  4. 4.
    Cerone P., Dragomir S.S.: A refinement of the Grü ss inequality and applications. Tamkang J. Math. 38, 37–49 (2007)MathSciNetMATHGoogle Scholar
  5. 5.
    Dragomir, S.S.: A survey on Cauchy–Bunyakovsky–Schwarz type discrete inequalities. J. Inequal. Pure Appl. Math. 4(3), Art. 63 (2003)Google Scholar
  6. 6.
    Dragomir S.S.: Bounds for the normalised Jensen functional. Bull. Aust. Math. Soc. 74, 471–478 (2006)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Mitroi F.-C.: Estimating the normalized Jensen functional. J. Math. Inequal. 5(4), 507–521 (2011)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Mitroi, F.-C.: Connection between the Jensen and the Chebychev functionals. In: Bandle, C., Gilanyi, A., Losonczi, L., Plum, M. (eds.) Inequalities and Applications 2010, Part 5, vol. 161, pp. 217–227. International Series of Numerical Mathematics, 1. Dedicated to the Memory of Wolfgang Walter, Birkhäuser, Basel (2012). doi: 10.1007/978-3-0348-0249-9_17
  9. 9.
    Niculescu C.P.: An extension of Chebyshev’s inequality and its connection with Jensen’s inequality. J. Inequal. Appl. 6, 451–462 (2001)MathSciNetMATHGoogle Scholar
  10. 10.
    Walker S.G.: On a lower bound for the Jensen inequality. SIAM J. Math. Anal. 46(5), 3151–3157 (2014). doi: 10.1137/140954015 MathSciNetCrossRefMATHGoogle Scholar

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© Springer Basel 2015

Authors and Affiliations

  • Flavia-Corina Mitroi-Symeonidis
    • 1
  • Nicuşor Minculete
    • 2
  1. 1.Faculty of Engineering SciencesLUMINA - University of South-East EuropeBucharestRomania
  2. 2.Transilvania University of BraşovBrasovRomania

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