Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-17T18:21:53.013Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalizations of a weighted trapezoidal inequality for monotonic functions and applications

Published online by Cambridge University Press:  17 February 2009

Kuei-Lin Tseng ,
Gou-Sheng Yang  and
Sever S. Dragomir
Kuei-Lin Tseng
Affiliation:
Department of Mathematics, Aletheia University, Tamsui 25103, Taiwan; e-mail: [email protected].
Gou-Sheng Yang
Affiliation:
Department of Mathematics, Tamkang University, Tamsui 25137, Taiwan.
Sever S. Dragomir
Affiliation:
School of Computer Science and Mathematics, Victoria University, PO Box 14428, MCMC 8001, Victoria, Australia; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we establish some generalizations of a weighted trapezoidal inequality for monotonic functions and give several applications for the r-moments, the expectation of a continuous random variable and the Beta and Gamma functions.

Keywords

trapezoidal inequalitymonotonic functionsr-momentsexpectation of a continuous random variablethe Beta and Gamma functions
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 4 , April 2007 , pp. 553 - 566
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Apostol, T. M., Mathematical Analysis, 2nd ed. (Addison-Wesley, Reading, Mass.-London-Don Mills, Ont., (1975)Google Scholar
[2]Barnett, N. S., Dragomir, S. S. and Pearce, C. E. M.,“A quasi-trapezoid inequality for double integrals”, ANZIAM J. 44 (2003) 355–364.CrossRefGoogle Scholar
[3]Cerone, P. and Dragomir, S. S., “Trapezoidal type rules from an inequalities point of view”, in Handbook of Analytic-Computational Methods in Applied Mathematics (ed. Anastassiou, G.), (CRC Press, New York, 2000) 65–134.Google Scholar
[4]Cerone, P., Dragomir, S. S. and Pearce, C. E. M., “A generalized trapezoid inequality for functions of bounded variation”, Turkish J. Math. 24 (2000) 147–163.Google Scholar
[5]Dragomir, S. S., “On the trapezoid quadrature formula for Lipschitzian mappings and applications”, Tamkang J. Math. 30 (1999) 133–138.CrossRefGoogle Scholar
[6]Dragomir, S. S., “On the trapezoid quadrature formula and applications”, Kragujevac J. Math. 23 (2001) 25–36.Google Scholar
[7]Dragomir, S. S., Cerone, P. and Sofo, A., “Some remarks on the trapezoid rule in numerical integration”, Indian J. Pure Appl. Math. 31 (2000) 475–494.Google Scholar
[8]Dragomir, S. S. and Peachey, T. C., “New estimation of the remainder in the trapezoidal formula with applications”, Stud. Univ. Babeş-Bolyai Math. (Cluj) 45 (2000) 31–42.Google Scholar
[9]Fejér, L., “Uberdie Fourierreihen, II”, Math. Natur. Ungar. Akad. Wiss. 24 (1906) 369–390.Google Scholar