Rocky Mountain Journal of Mathematics

On the Weighted Generalization of the Hermite-Hadamard Inequality and its Applications

Shanhe Wu

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Rocky Mountain J. Math. Volume 39, Number 5 (2009), 1741-1749.

Dates
First available in Project Euclid: 8 October 2009

Permanent link to this document
http://projecteuclid.org/euclid.rmjm/1255008581

Digital Object Identifier
doi:10.1216/RMJ-2009-39-5-1741

Zentralblatt MATH identifier
05614530

Mathematical Reviews number (MathSciNet)
MR2546662

Subjects
Primary: 26D15: Inequalities for sums, series and integrals 26D20: Other analytical inequalities 26D07: Inequalities involving other types of functions

Keywords
Hermite-Hadamard inequality Jensen's inequality integral inequality convex function generalization refinement

Citation

Wu, Shanhe. On the Weighted Generalization of the Hermite-Hadamard Inequality and its Applications. Rocky Mountain Journal of Mathematics 39 (2009), no. 5, 1741--1749. doi:10.1216/RMJ-2009-39-5-1741. http://projecteuclid.org/euclid.rmjm/1255008581.


Export citation

References

  • M. Bessenyei and Z. Páles, Characterizations of convexity via Hadamard's inequality, Math. Inequal. Appl. 9 (2006), 53-62.
  • L. Dedić, C.E.M. Pearce and J. Pečarić, The Euler formula and convex functions, Math. Inequal. Appl. 3 (2000), 211-221.
  • S.S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), 91-95.
  • --------, Two new mappings associated with Hadamard's inequality for convex functions, Appl. Math. Lett. 11 (1998), 33-38.
  • S.S. Dragomir, Y.J. Cho and S.S. Kim, Inequalities of Hadamard's type for Lipschitzian mappings and their applications, J. Math. Anal. Appl. 245 (2000), 489-501.
  • S.S. Dragomir and C.E.M. Pearce, Quasilinearity & Hadamard's inequality, Math. Inequal. Appl. 5 (2002), 463-471.
  • L. Fejér, Über die Fourierreihen, II, Math. Naturwiss. Anz. Ungar. Akad. Wiss. 24 (1906), 369-390 (in Hungarian).
  • P.M. Gill, C.E.M. Pearce and J. Pečarić, Hadamard's inequality for $r$-convex functions, J. Math. Anal. Appl. 215 (1997), 461-470.
  • A.M. Mercer, Hadamard's inequality for a triangle, a regular polygon and a circle, Math. Inequal. Appl. 5 (2002), 219-223.
  • C.E.M. Pearce and J. Pečarić, Inequalities for differentiable mappings with applications to special means and quadrature formula, Appl. Math. Lett. 13 (2000), 51-55.
  • C.E.M. Pearce, J. Pečarić and V. Šimić, Stolarsky means and Hadamard's inequality, J. Math. Anal. Appl. 220 (1998), 99-109.
  • C.E.M. Pearce and A.M. Rubinov, $P$-functions, quasi-convex functions, and Hadamard-type inequalities, J. Math. Anal. Appl. 240 (1999), 92-104.
  • J.E. Pečarić, F. Proschan and Y.L. Tong, Convex functions, partial orderings, and statistical applications, Academic Press, New York, 1992.
  • M.B. Sun and X.P. Yang, Generalized Hadamard's inequality and r-convex functions in Carnot groups, J. Math. Anal. Appl. 294 (2004), 387-398.
  • L.C. Wang, On extensions and refinements of Hermite-Hadamard inequalities for convex functions, Math. Inequal. Appl. 6 (2003), 659-666.
  • G.S. Yang and D.Y. Hwang, Some inequalities for differentiable convex and concave mappings, Comput. Math. Appl. 47 (2004), 207-216.
  • G.S. Yang and K.L. Tseng, Inequalities of Hadamard's type for Lipschitzian mappings, J. Math. Anal. Appl. 260 (2001), 230-238.
  • --------, On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl. 239 (1999), 180-187.