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Inequalities for a weighted multiple integral. (English) Zbl 0966.26013
Summary: In the article, using Taylor’s formula for functions of several variables, the author establishes some inequalities for the weighted multiple integral of a function defined on an $m$-dimensional rectangle, if its partial derivatives of $(n+1)$th-order remain between bounds. Using this result, Iyengar’s inequality is generalized and related results can be deduced.

26D15Inequalities for sums, series and integrals of real functions
26B15Integration: length, area, volume (several real variables)
Full Text: DOI
[1] Agarwal, R. P.; Dragomir, S. S.: An application of hayashi’s inequality for differentiable functions. Comput. math. Appl. 32, 95-99 (1996) · Zbl 0874.26017
[2] Cerone, P.; Dragomir, S. S.: On a weighted generalization of iyengar type inequalities involving bounded first derivative. RGMIA research report collection 2, 147-157 (1999)
[3] Cerone, P.; Dragomir, S. S.: Lobatto type quadrature rules for functions with bounded derivative. RGMIA research report collection 2, 133-146 (1999) · Zbl 0958.26011
[4] Cui, L. -H.; Guo, B. -N.: On proofs of an integral inequality and its generalizations. J. zhengzhou grain college 17, 152-154 (1996)
[5] Guo, B. -N.; Qi, F.: Proofs of an integral inequality. Math. informatics quart. 7, 182-184 (1997)
[6] Iyengar, K. S. K.: Note on an inequality. Math. student 6, 75-76 (1938) · Zbl 64.0209.02
[7] Kuang, J. -C.: Chap. 8. (1993)
[8] Milovanović, G. V.; Pečarić, J. E.: Some considerations on iyengar’s inequality and some related applications. Univ. beograd. Publ. elektrotehn. Fak. ser. Mat. fiz. 544--576, 166-170 (1976)
[9] Mitrinović, D. S.: Analytic inequalities. (1970)
[10] Mitrinović, D. S.; Pečarić, J. E.; Fink, A. M.: Chap. XV. (1991)
[11] Qi, F.: Inequalities for an integral. Math. gaz. 80, 376-377 (1996)
[12] Qi, F.: Further generalizations of inequalities for an integral. Univ. beograd. Publ. elektrotehn. Fak. ser. Mat. 8, 79-83 (1997) · Zbl 1018.26012
[13] Qi, F.: Inequalities for a multiple integral. Acta math. Hungar. 84, 19-26 (1999) · Zbl 0963.26008
[14] Qi, F.: Inequalities for a weighted integral. RGMIA research report collection 2 (1999) · Zbl 0963.26008
[15] Vasić, P. M.; Milonanović, G. V.: On an inequality of iyengar. Univ. beograd. Publ. elektrotehn. Fak. ser. Mat. fiz. 544--576, 18-24 (1976)
[16] Guo, B. -N.; Qi, F.: Estimates for an integral in lp norm of the (n+1)th derivatives of its integrand. RGMIA research report collection 3 (2000)