Rocky Mountain Journal of Mathematics

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

Shanhe Wu

Full-text: Open access

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

Mathematical Reviews number (MathSciNet)
MR2546662

Zentralblatt MATH identifier
05614530

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 J. Math. 39 (2009), no. 5, 1741--1749. doi:10.1216/RMJ-2009-39-5-1741. http://projecteuclid.org/euclid.rmjm/1255008581.


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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.