A new generalization of the trapezoid formula for n-time differentiable mappings and applications

• Autorzy: Cerone P. , Dragomir S. , Roumeliotis J. , Sunde J.
• Języki publikacji: EN

Abstrakty

EN

A new generalization of the trapezoid formula for n-time differentiable mappings and applications in Numerical Analysis are given.

Słowa kluczowe

EN

trapezoid inequality; numerical analysis

PL

nierówności trapezowe; analiza numeryczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2000
• Tom: Vol. 33, nr 4
• Strony: 719--736
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Cerone P.

• Department of Computer and Mathematical Sciences, Victoria University of Technology, PO Box 14428 MCMC, Melbourne, Victoria 8001

autor

Dragomir S.

• Department of Computer and Mathematical Sciences, Victoria University of Technology, PO Box 14428 MCMC, Melbourne, Victoria 8001

autor

Roumeliotis J.

• Department of Computer and Mathematical Sciences, Victoria University of Technology, PO Box 14428 MCMC, Melbourne, Victoria 8001

autor

Sunde J.

• Communication Division, DSTO, PO Box 1500 Salisbury, SA 5108

Bibliografia

• [1] P. Cerone, S. S. Dragomir and J. Roumeliotis, Some Ostrowski type inequalities for n-time differentiable mappings and applications, Demonstratio Math., 32(4) (1999), 697-712.
• [2] S. S. Dragomir, On the trapezoid formula for Lipschitzian mappings and applications, Tamkang J . Math., 30(2) (1999), 133-138.
• [3] S. S. Dragomir, P. Cerone and A. Sofo, Some remarks on the trapezoid rule in numerical integration, Indian J . Pure Appl. Math., 31(5) (2000), 415-494.
• [4] S. S. Dragomir and T. C. Peachey, New estimation of the remainder in the trapezoidal formula with applications, accepted Studia Math. Babes-Bolyai Univ.
• [5] P. Cerone, S. S. Dragomir and C. E. M. Pearce, A generalized trapezoid inequality for functions of bounded variation, Turkish. J . Math. 24 (2000), 1-17.
• [6] N. S. Barnett, S. S. Dragomir and C. E. M. Pearce, A quasi-trapezoid inequality for double integrals, submitted J . Austral. Math. Sec. (B).
• [7] S. S. Dragomir and A. Mc Andrew, On trapezoid inequality via a Griiss type result and applications, accepted in Tamkang J. Math.
• [8] S. S. Dragomir, J. E. Pečarić and S. Wang, The unified treatment of trapezoid, Simpson and Ostrowski type inequality for monotonic mappings and applications, Math. Comput. Modelling, 31 (2000), 61-70.
• [9] D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Inequalities for Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1994.
• [10] V. Čuljak, C.E.M. Pearce and J. P. Pečarić, The unified treatment of some inequalities of Ostrowski and Simpson's type, submitted.
• [11] S. S. Dragomir, A Taylor like formula and application in numerical integration, submitted.
• [12] P. Cerone and S. S. Dragomir, Three point quadrature rules involving, at most, a first derivative, Preprint. RGMIA Res. Rep. Coll., 2(4) (1999), Article 8.
• [13] J. E. Pečarić, F. Proschan and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Presss, 1992.
• [14] M. Matic, J. E. Pečarić and N. Ujevic, On New estimation of the remainder in Generalised Taylor's Formula, M.I.A., Vol. 2 No. 3 (1999), 343-361.