Some integral inequalities related to Wirtinger's result for \(p\)-norms
- S. S. Dragomir sever.dragomir@vu.edu.au
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DOI:
https://doi.org/10.4067/S0719-06462021000300457Abstract
In this paper we establish several natural consequences of some Wirtinger type integral inequalities for \(p\)-norms. Applications related to the trapezoid unweighted inequalities, of Grüss' type inequalities and reverses of Jensen's inequality are also provided.
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M. W. Alomari, “On Beesack–Wirtinger Inequality”, Results Math., vol. 73, no. 2, pp. 1213– 1225, 2017.
P. R. Beesack, “Extensions of Wirtinger‘s inequality”, Trans. R. Soc. Can., vol. 53, pp. 21–30, 1959.
P. L. Chebyshev, “Sur les expressions approximatives des intégrales dèfinis par les autres prises entre les même limites”, Proc. Math. Soc. Charkov, vol. 2, pp. 93–98, 1882.
J. B. Díaz and F. T. Metcalf, “Variations on Wirtinger‘s inequality”, in Inequalities, New York: Academic Press, 1967, pp. 79–103.
P. Drábek and R. Manásevich, “On the closed solution to some nonhomogeneous eigenvalue problems with p-Laplacian”, Differential Integral Equations, vol. 12, no. 6, pp. 773–788, 1999.
S. S. Dragomir, “A Grüss type inequality for isotonic linear functionals and applications”, Demonstratio Math., vol. 36, no. 3, pp. 551–562, 2003.
S. S. Dragomir, “Some integral inequalities related to Wirtinger‘s result”, Preprint, RGMIA Res. Rep. Coll., vol. 21, art. 60, 2018.
R. Giova, “An estimate for the best constant in the Lp-Wirtinger inequality with weights”, J. Func. Spaces Appl., vol. 6, no. 1, pp. 1–16, 2008.
R. Giova and T. Ricciardi, “A sharp weighted Wirtinger inequality and some related functional spaces”, Bull. Belg. Math. Soc. Simon Stevin, vol. 17, no. 2, pp. 209–218, 2010.
G. Grüss, “Ìber das Maximum des absoluten Betrages von Ìber das Maximum des absoluten Betrages von (frac{1}{b-a}int limits_{a}^{b}f(x)g(x)dx-frac{1}{left( b-aright) ^{2}} int limits_{a}^{b}f(x)dxint limits_{a}^{b}g(x)dx)”, Math. Z., vol. 39, no. 1, pp. 215–226, 1935
J. Jaroš, “On an integral inequality of the Wirtinger type”, Appl. Math. Letters, vol. 24, no. 8, pp. 1389–1392, 2011.
C. F. Lee, C. C. Yeh, C. H. Hong and R. P. Agarwal, “Lyapunov and Wirtinger inequalities”, Appl. Math. Lett., vol. 17, no. 7, pp. 847–853, 2004.
A. LupaÅŸ, “The best constant in an integral inequality”, Mathematica (Cluj), vol. 15, no. 38, pp. 219–222, 1973.
A. M. Ostrowski, “On an integral inequality”, Aequationes Math., vol. 4, pp. 358–373, 1970.
T. Ricciardi, “A sharp weighted Wirtinger inequality”, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), vol. 8, no. 1, pp. 259–267, 2005.
C. A. Swanson, “Wirtinger‘s inequality”, SIAM J. Math. Anal., vol. 9, no. 3, pp. 484–491, 1978.
S.-E. Takahasi, T. Miura and T. Hayata, “On Wirtinger‘s inequality and its elementary proof”, Math. Inequal. Appl., vol. 10, no. 2, pp. 311–319, 2007.
S. Takeuchi, “Generalized elliptic functions and their application to a nonlinear eigenvalue problem with p-Laplacian”, J. Math. Anal. Appl., vol. 385 , no. 1, pp. 24–35, 2012.
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