A Companion of the generalized trapezoid inequality and applications

• Autorzy: Alomari M. W.

Identyfikatory

DOI

10.7862/rf.2013.1

• Języki publikacji: EN

Abstrakty

EN

A sharp companion of the generalized trapezoid inequality is introduced. Applications to quadrature formula are pointed out.

Słowa kluczowe

EN

trapezoid inequality; midpoint inequality; Ostrowski's inequality; bounded variation; Lipschitzian mapping; monotonic mappings

PL

nierówności trapezoidowe; nierówności; nierówności Ostrowskiego; wariacja ograniczona; odwzorowania

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2013
• Tom: Vol. 36
• Strony: 5--15
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Alomari M. W.

• Department of Mathematics, Faculty of Science, Jerash University, 26150 Jerash, Jordan

Bibliografia

• [1] M.W. Alomari, New sharp inequalities of Ostrowski and generalized trapezoid type for the Riemann-Stieltjes integrals and applications, Ukrainian Math. J., to appear.
• [2] M.W. Alomari, A companion of Ostrowski's inequality for the Riemann-Stieltjes integral [...], where ƒ is of bounded variation and u is of r-H-Hölder type and applications, Appl. Math. Comput., 219 (2013), 4792-4799.
• [3] M.W. Alomari, A companion of Dragomir's generalization of Ostrowski's inequality and applications in numerical integration, Ukrainian Mathematical Journal, 64(4) (2012), 491-510.
• [4] M.W. Alomari, A companion of Ostrowski's inequality for mappings whose first derivatives are bounded and applications in numerical integration, Kragujevac Journal of Mathematics, 36 (2012), 77-82.
• [5] M.W. Alomari, A generalization of companion inequality of Ostrowski's type for mappings whose first derivatives are bounded and applications and in numerical integration, Trans. J. Math. Mech., 4(2) (2012), 103-109.
• [6] P. Cerone, S.S. Dragomir, C.E.M. Pearce, A generalized trapezoid inequality for functions of bounded variation, Turk. J. Math., 24 (2000), 147-163.
• [7] P. Cerone and S.S. Dragomir, Trapezoidal-type rules from an inequalities point of view, Handbook of Analytic-Computational Methods in Applied Mathematics, Editor: G. Anastassiou, CRC Press, New York (2000), 65-134.
• [8] P. Cerone and S.S. Dragomir, Midpoint-type rules from an inequalities point of view, Handbook of Analytic-Computational Methods in Applied Mathematics, Editor: G. Anastassiou, CRC Press, New York (2000), 135-200.
• [9] S.S. Dragomit, Ostrowski integral inequality for mappings of bounded variation, Bull. Austral. Math. Soc., 60 (1999) 495-508.
• [10] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000. Online: http://www.staff.vu.edu.au/RGMIA/monographs/hermite hadamard.html
• [11] S.S. Dragomir and Th.M. Rassias (Ed.), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publishers, Dordrecht, 2002.
• [12] K.L. Tseng, G.S. Yang, S.S. Dragomir, Generalizations of weighted trapezoidal inequality for mappings of bounded variation and their applications, Mathematical and Computer Modelling, 40 (2004) 77-84.
• [13] A. Guessab and G. Schmeisser, Sharp integral inequalities of the Hermite-Hadamard type, J. Approx. Th., 115 (2002), 260-288.
• [14] S.S. Dragomir, A companion of Ostrowski's inequality for functions of bounded variation and applications, RGMIA Preprint, Vol. 5 Supp. (2002) article No. 28. [http://ajmaa.org/RGMIA/papers/v5e/COIFBVApp.pdf]
• [15] Z. Liu, Another generalization of weighted Ostrowski type inequality for mappings of bounded variation, Appl. Math. Lett. accepted DOI: 10.1016/j.aml.2011.09.020
• [16] W.-J. Liu, Some Weighted Integral Inequalities with a Parameter and Applications, Acta Appl Math., 109 (2010), 389-400.