Opuscula Math. 35, no. 3 (2015), 411-419
http://dx.doi.org/10.7494/OpMath.2015.35.3.411

 
Opuscula Mathematica

Hermite-Hadamard type inequalities for Wright-convex functions of several variables

Dorota Śliwińska
Szymon Wąsowicz

Abstract. We present Hermite-Hadamard type inequalities for Wright-convex, strongly convex and strongly Wright-convex functions of several variables defined on simplices.


Referred to by Corrigendum to "Hermite-Hadamard type inequalities for Wright-convex functions of several variables"

Article: Opuscula Math. 36, no. 2 (2016), 279-280, http://dx.doi.org/10.7494/OpMath.2016.36.2.279


Keywords: convex functions, Wright-convex functions, strongly Wright-convex functions, Hermite-Hadamard inequality.

Mathematics Subject Classification: 26B25, 26D15, 39B62, 65D32.

Full text (pdf)

  1. M. Bessenyei, The Hermite-Hadamard inequality on simplices, Amer. Math. Monthly 115 (2008), 339-345.
  2. S.S. Dragomir, C.E.M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2002.
  3. A. Guessab, G. Schmeisser, Convexity results and sharp error estimates in approximate multivariate integration, Math. Comp. 73 (2004), 1365-1384.
  4. J.B. Hiriart-Urruty, C. Lemaréchal, Fundamentals of convex analysis, Springer-Verlag, Berlin Heidelberg, 2001.
  5. N. Merentes, K. Nikodem, Remarks on strongly convex functions, Aequationes Math. 80 (2010), 193-199.
  6. N. Merentes, K. Nikodem, S. Rivas, Remarks on strongly Wright-convex functions, Ann. Polon. Math. 102 (2011), 271-278.
  7. E. Neuman, Inequalities involving multivariate convex functions II, Proc. Amer. Math. Soc. 109 (1990), 965-974.
  8. C.T. Ng, Functions generating Schur-convex sums, [in:] General inequalities, 5 (Oberwolfach, 1986), volume 80 of Internat. Schriftenreihe Numer. Math., pp. 433-438, Birkhäuser, Basel, 1987.
  9. C.P. Niculescu, L.E. Persson, Convex Functions and Their Applications. A Contemporary Approach, Springer, New York 2006.
  10. A. Olbryś, On some inequalities equivalent to the Wright convexity, submitted.
  11. B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Soviet Math. Dokl. 7 (1966), 72-75.
  12. Sz. Wąsowicz, A. Witkowski, On some inequality of Hermite-Hadamard type, Opuscula Math. 32 (2012), 591-600.
  13. Sz. Wąsowicz, Hermite-Hadamard-type inequalities in the approximate integration, Math. Inequal. Appl. 11 (2008), 693-700.
  • Dorota Śliwińska
  • University of Bielsko-Biała, Department of Mathematics and Computer Science, Willowa 2, 43-309 Bielsko-Biała, Poland
  • Szymon Wąsowicz
  • University of Bielsko-Biała, Department of Mathematics and Computer Science, Willowa 2, 43-309 Bielsko-Biała, Poland
  • Communicated by Zbigniew Szkutnik.
  • Received: 2013-12-19.
  • Revised: 2014-09-29.
  • Accepted: 2014-09-29.
  • Published online: 2014-12-15.
Opuscula Mathematica - cover

Cite this article as:
Dorota Śliwińska, Szymon Wąsowicz, Hermite-Hadamard type inequalities for Wright-convex functions of several variables, Opuscula Math. 35, no. 3 (2015), 411-419, http://dx.doi.org/10.7494/OpMath.2015.35.3.411

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.