On the Jensen Functional and Strong Convexity

  • Flavia-Corina Mitroi-Symeonidis
  • Nicuşor Minculete


In this note we describe some results concerning upper and lower bounds for the Jensen functional. We use several known and new results to shed light on the concept of a strongly convex function.


Jensen functional Strongly convex function 

Mathematics Subject Classification

Primary 26B25 Secondary 26D15 



The first author is grateful to Professors S. Abramovich and S.S. Dragomir for the interesting and productive mathematical discussions which have led to some of the questions this work is intended to answer.


  1. 1.
    Dragomir, S.S.: Bounds for the normalised Jensen functional. Bull. Austral. Math. Soc. 74, 471–478 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Hiriart-Urruty, J.B., Lemaréchal, C.: Fundamentals of Convex Analysis. Springer, Berlin Heidelberg (2001)CrossRefzbMATHGoogle Scholar
  3. 3.
    Merentes, N., Nikodem, K.: Remarks on strongly convex functions. Aequationes Math. 80(1–2), 193–199 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Mitroi, F.-C.: Estimating the normalized Jensen functional. J. Math. Inequal. 5(4), 507–521 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Mitroi, F.-C.: Connection between the Jensen and the Chebychev functionals, International Series of Numerical Mathematics, 1. In: Bandle, C., Gilanyi, A., Losonczi, L., Plum, M. (eds.). Inequalities and Applications 2010, Part 5, Dedicated to the Memory of Wolfgang Walter, vol. 161, pp. 217–227. Birkhäuser, Basel,(2012). doi: 10.1007/978-3-0348-0249-9_17
  6. 6.
    Nikodem, K., Páles, Zs.: On t-Convex Functions. Real Analysis Exchange 29(1), 219-228 (2003/2004)Google Scholar
  7. 7.
    Polyak, B.T.: Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Soviet. Math. Dokl. 7, 72–75 (1966)Google Scholar
  8. 8.
    Rajba, T., Wąsowicz, Sz: Probabilistic characterization of strong convexity. Opusc. Math. 31(1), 97–103 (2011)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2016

Authors and Affiliations

  • Flavia-Corina Mitroi-Symeonidis
    • 1
  • Nicuşor Minculete
    • 2
  1. 1.Faculty of Engineering SciencesLUMINA - University of South-East EuropeBucharestRomania
  2. 2.Department of Mathematics and Computer ScienceTransilvania UniversityBraşovRomania

Personalised recommendations