Abstract
AbstractWe observe that every quadrature of numerical integration together with a strictly increasing and continuous function generates a mean and then we study this family of means. We characterize the functions which generate weighted arithmetic means in this way and we show how to obtain comparison type theorems for means generated by different quadratures.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,General Mathematics
Reference20 articles.
1. Alzer, H.: Inequalities for mean values in two variables Real Anal. Exchange 41(1), 101–122 (2016)
2. Berrone, L.R., Moro, J.: Lagrangian means. Aequ. Math. 55, 217–226 (1998)
3. Bessenyei, M., Páles, Z.S.: Higher-order generalizations of Hadamard’s inequality. Publ. Math. (Debrecen) 61(3–4), 623–643 (2002)
4. Bullen, P.S., Mitrinović, D.S., Vasić, P.M.: Means and Their Inequalities. D. Reidel Publishing Company, Dordrecht (1988)
5. Denuit, M., Lefevre, C., Shaked, M.: The s-convex orders among real random variables, with applications. Math. Inequal. Appl. 1(4), 585–613 (1998)