Levinson’s Type Generalization of the Edmundson–Lah–Ribarič Inequality

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• 作者：Rozarija Jakšić ; Josip Pečarić
• 关键词：Primary 60E15 ; Secondary 26A51 ; 26E60 ; Edmundson–Madansky and Lah–Ribarič inequalities ; Levinson’s inequality ; convex functions ; exponential convexity ; means
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：13
• 期：1
• 页码：483-496
• 全文大小：539 KB
• 参考文献：1.Aglić Aljinović, A., Čivljak, A., Kovač, S., Pečcarić, J., Ribičić Penava, M.: General integral identities and related inequalities/arising from weighted montgomery identity, Monographs in inequalities 5, Element, Zagreb, (2013)r>2.Baloch, I.A., Pečarić, J., Praljak, M.: Generalization of Levinson’s inequality. J. Math. Inequal. (to appear)r>3.Beesack P.R., Pečarić J.E.: On the Jessen’s inequality for convex functions. J. Math. Anal. 110, 536–552 (1985)CrossRef MATH r>4.Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming, Springer New York, (1997)r>5.Bullen, P.S.: An inequality of N. Levinson., Univ. Beograd. Publ. Elektrotehn.. Fak. Ser. Mat. Fiz. No. 421–460, 109–112 (1985)r>6.Edmundson, H.P.: Bounds on the expectation of a convex function of a random variable. The Rand Corporation, Paper No. 982 (1956), Santa Monica, Californiar>7.Franjić, I., Pečarić, J., Perić, I., Vukelić, A.: Euler integral identity, quadrature formulae and error estimations From the point of view of inequality theory, Monographs in inequalities 2, Element, Zagreb, (2011)r>8.Fujii, M.,Mičić Hot, J., Pečarić, J., Seo, Y.: Recent developments of mond-peari method in operator inequalities inequalities for bounded selfadjoint operators on a Hilbert space II., Monographs in inequalities 4, Element, Zagreb, 2012., pp. 332r>9.Furuta T., Mičić Hot J., Pečarić J., Seo Y.: Mond-Peari method in operator inequalities inequalities for bounded selfadjoint operators on a Hilbert space. Monographs in inequalities 1, Element (2005)r>10.Krnić, M., Pečarić, J., Perić, I., Vuković, P.: Recent advances in Hilbert-type inequalities a unified treatment of Hilbert-type inequalities, Monographs in inequalities 3, Element, Zagreb, 2012., pp. 246r>11.Krulić Himmelreich K., Pečarić J., Pokaz D.: Inequalities of Hardy and Jensen New Hardy type inequalities with general kernels, Monographs in inequalities 6. Element, Zagreb (2013)r>12.Kuhn D.: Generalized Bounds for Convex Multistage Stochastic Programs. Springer, Berlin (2005)MATH r>13.Lah, P., Ribarič, M.: Converse of Jensen’s inequality for convex functions. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 412–460, 201–205r>14.Levinson N.: Generalisation of an inequality of Ky Fan. J. Math. Anal. Appl. 8, 133–134 (1964)CrossRef MathSciNet MATH r>15.Madansky A.: Bounds on the expectation of a convex function of a multivariate random variable. Ann. Math. Stat. 30, 743–746 (1959)CrossRef MathSciNet MATH r>16.Mercer A.M.D.: Short proof of Jensen’s and Levinson’s inequality. Math. Gaz. 94, 492–495 (2010)r>17.Pečarić, J.: On an inequality of N. Levinson. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 678-715, 71–74r>18.Pečarić, J., Praljak, M., Witkowski, A.: Generalized Levinson’s inequality and exponential convexity. Opusc. Math. (to appear)r>19.Pečarić J.E., Proschan F., Tong Y.L.: Convex Functions, Partial Orderings And Statistical Applications. Academic Press Inc., San Diego (1992)MATH r>20.Witkowski, A.: On Levinson’s inequality. RGMIA Research Report Collection 15, Art. 68 (2012)r>
• 作者单位：Rozarija Jakšić (1) r> Josip Pečarić (1) r>r>1. Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10 000, Zagreb, Croatia r>
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematicsr>Mathematicsr>
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

In this paper the authors give a brief historical remark on Edmundson–Madansky and Lah–Ribarič inequalities, which are both special cases of the same inequality, and unify them under the name of Edmundson–Lah–Ribarič inequality. Furthermore, the authors also give a Levinson’s type generalization of the Edmundson–Lah–Ribarič inequality, as well as some refinements of the obtained results by constructing certain exponentially convex functions. Mathematics Subject Classification Primary 60E15 Secondary 26A51 26E60