Skip to main content Accessibility help
×
Home

Generalized Hadamard's inequalities based on general Euler 4-point formulae

  • M. Klaričić Bakula and J. Pečarić

Abstract

We present a general closed 4-point quadrature rule based on Euler-type identities. We use this rule to prove a generalization of Hadamard's inequalities for (2r)-convex functions (r ≥ 1).

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Generalized Hadamard's inequalities based on general Euler 4-point formulae
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Generalized Hadamard's inequalities based on general Euler 4-point formulae
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Generalized Hadamard's inequalities based on general Euler 4-point formulae
      Available formats
      ×

Copyright

References

Hide All
[1]Abramowitz, M. and Stegun, I. A. (eds.), Handbook of mathematical functions with formulae, graphs and mathematical tables, Applied Math. Series 55, 4th printing (National Bureau of Standards, Washington, 1965).
[2]Berezin, I. S. and Zhidkov, N. P., Computing Methods, Vol. 1 (Pergamon Press, Oxford, 1965).
[3]Bullen, P. S., “Error estimates for some elementary quadrature rules”, Univ. Beograd Publ. Elektrotehn. Fak., Ser. Mat. Fiz. 602633 (1978) 97103.
[4]Dedić, Lj., Matić, M. and Pečarić, J., “On generalizations of Ostrowski inequality via some Euler-type identities”, Math. Inequal. Appl. 3 (2000) 337353.
[5]Dedić, Lj., Matić, M. and Pečarić, J., “On Euler trapezoid rule”, Appl. Math. Comput. 123 (2001) 3762.
[6]Dedić, Lj., Matić, M., Pečarić, J. and Vukelić, A., “Hadamard-type inequalities via some Euler-type identities—Euler bitrapezoid formulae”, Nonlinear Stud. 8 (2001) 343372.
[7]Klaričić Bakula, M., Pečarić, J. and Vukelić, A., “Interpolation of periodic functions and applications on some integration formulae of interpolatory type”, Bull. Math. Soc. Sci. Math. Roumanie 48 (2005) 261275.
[8]Pečarić, J. and Vukelić, A., Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions, Functional Equations, Inequalities and Applications (Kluwer, Dordrecht, 2003).
[9]Pečarić, J. E., Perić, I. and Vukelić, A., “Sharp integral inequalities based on general Euler two-point formulae”, ANZIAM J. 46 (2005) 555574.
[10]Pečarić, J. E., Proschan, F. and Tong, Y. L., Convex functions, partial orderings, and statistical applications (Academic Press, New York, 1992).
[11]Roberts, A. W. and Varberg, D. E., Convex Functions (Academic Press, New York, 1973).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Related content

Powered by UNSILO

Generalized Hadamard's inequalities based on general Euler 4-point formulae

  • M. Klaričić Bakula and J. Pečarić

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.