New Ostrowski and Gruss type inequalities for double integrals

• Autorzy: Pachpatte B.
• Języki publikacji: EN

Abstrakty

EN

In the present paper we establish new Ostrowski and Grüss type inequ- alities for double integrals involving three functions and their partial derivatives. The discrete Ostrowski and Grüss type inequalities for double sums are also given.

Słowa kluczowe

EN

Gruss type inequalities; Ostrowski type inequalities; double integrals; partial derivatives; difference operators; discrete analogues

PL

nierówności typu Grussa; nierówności typu Ostrowskiego; całki podwójne; operatory różnicowe; pochodne cząstkowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 4
• Strony: 783--791
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Pachpatte B.

• 57 Shri Niketan Colony Near Abhinay Talkies Aurangabad 431 001 (Maharashtra), India,

Bibliografia

• [1] N. S. Barnett and S. S. Dragomir, An Ostrowski type inequality for double integrals and applications for cubature formulae, Soochow J. Math. 27 (1) (2001), 1–10.
• [2] S. S. Dragomir and T. M. Rassias (Eds.), Ostrowski Type Inequalities and Applications in Numerical Integration, Kluwer Academic Publishers, Drodrecht, 2002.
• [3] G. Gruss, Über das maximum des absoluten Betrages von 1/b - a ?b\a f (x) g (x) dx -1(b - a)2 ?b\a f (x) dx ? b\a g (x) dx, ath. Z. 39 (1935), 215–226.
• [4] D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.
• [5] D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Inequalities for Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1994.
• [6] A. M. Ostrowski, Über die Absolutabweichung einer differentiebaren Functions van ihrem Integralmittelwert, Comment. Math. Hel. 10 (1938), 226–227.
• [7] B. G. Pachpatte, On a new Ostrowski type inequality in two independent variables, Tamkang J. Math. 32 (1) (2001), 45–49.
• [8] B. G. Pachpatte, On Grüss type inequalities for double integrals, J. Math. Anal. Appl. 267 (2002), 454–459.
• [9] B. G. Pachpatte, New weighted multivariate Grüss type inequalities, J. Inequal. Pure and Appl. Math. 4 (5) Art. 108, 2003.
• [10] B. G. Pachpatte, On Grüss type discrete inequalities,Math. Ineq. Appl. 7 (1) (2004), 13–17