Difference between weighted integral means

• Autorzy: Cerone P.
• Języki publikacji: EN

Abstrakty

EN

Weighted integral means over [c, d] and [a, b] where [c, d] C [a, 6] are compared in the current work by determining bounds for their difference in terms of a variety of norms. The bounds are obtained and involve the behaviour of at most the first derivative. Previous work for unweighted integral means is recaptured as particular cases if the weights are taken to be unity. By a limiting shrinking of the subinterval [c, d] to a single point, weighted Ostrowski type inequalities are shown to be recaptured, under certain conditions as particular instances of the current development.

Słowa kluczowe

EN

weighted integral means; bounds; weighted Ostrowski inequality

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 2
• Strony: 251--265
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Cerone P.

• School of Communications And Informatics, Victoria University of Technology, PO BOX 14428, Melbourne City Mc, Victoria 8001, Australia

Bibliografia

• [1] G. A. Abnastassiou, Ostrowski type inequalities, Proc. Amer. Math. Soc. 123(12) (1999), 3775-3781.
• [2] N. S. Barnett, P. Cerone, S. S. Dragomir and A. M. Fink, Comparing two integral means for absolutely continuous mappings whose derivatives are in L ∞ [a,b] and applications, Comput. Math. Appl. (accepted).
• [3] P. Cerone and S. S. Dragomir, Differences between means with bounds from a Riemann-Stieltjes integral, Comput. Math. Appl. (accepted).
• [4] P. Cerone and S. S. Dragomir, On some inequalities arising from Montgomery's identity, J. Comp. Anal. Appl. (accepted).
• [5] P. Cerone and S. S. Dragomir, Three point quadrature rules involving, at most, a first derivative, (submitted) (ON LINE: http://rgmia.vu.edu.au/v2n4.html).
• [6] S. S. Dragomir, On the Ostrowski's integral inequality for mappings with bounded variation and applications, Math. Ineq. & Appl. 4(1) (2001), 59-66. (ON LINE: http://rgmia.vu.edu.au/v2n1.html).
• [7] S. S. Dragomir, Ostrowski inequality for monotonous mappings and applications, J. KSIAM 3(1) (1999), 127-135.
• [8] S. S. Dragomir, The Ostrowski's integral inequality for Lipschitzian mappings and applications, Comput. Math. Appl. 38 (1999), 33-37.
• [9] S. S. Dragomir, The Ostrowski integral inequality for mappings of bounded variation, Bull. Austral. Math. Soc. 60 (1999), 495-508.
• [10] S. S. Dragomir and S. Wang, A new inequality of Ostrowski's type in Lp-norm and applications to some special means and to some numerical quadrature rules, Indian J. Math. 40(3) (1998), 299-304.
• [11] A. M. Fink, Bounds on the derivative of a function from its averages, Czech. Math. J. 42 (1992), 289-310.
• [12] M. Matić, J. E. Pečarić and N. Ujević, Generalisation of weighted version of Ostrowski inequality and some related results, J. Ineq. & Appl 5 (2000), 639-666.
• [13] D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1994.
• [14] A. Ostrowski, Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert, Comment. Math. Hei 10 (1938), 226-227.