Pavić, Zlatko Inequalities of convex functions and self-adjoint operators. (English) Zbl 1300.47025 J. Oper. 2014, Article ID 382364, 5 p. (2014). Summary: The paper offers generalizations of the Jensen-Mercer inequality for self-adjoint operators and generally convex functions. The obtained results are applied to define the quasi-arithmetic operator means without using operator convexity. The version of the harmonic-geometric-arithmetic operator mean inequality is derived as an example. MSC: 47A63 Linear operator inequalities 39B62 Functional inequalities, including subadditivity, convexity, etc. × Cite Format Result Cite Review PDF Full Text: DOI References: [1] C. Davis, “A Schwarz inequality for convex operator functions,” Proceedings of the American Mathematical Society, vol. 8, pp. 42-44, 1957. · Zbl 0080.10505 · doi:10.2307/2032808 [2] M. D. Choi, “A Schwarz inequality for positive linear maps on C*-algebras,” Illinois Journal of Mathematics, vol. 18, pp. 565-574, 1974. · Zbl 0293.46043 [3] F. Hansen, J. Pe, and I. Perić, “Jensen’s operator inequality and its converses,” Mathematica Scandinavica, vol. 100, no. 1, pp. 61-73, 2007. · Zbl 1151.47025 [4] J. Mićić, Z. Pavić, and J. Pe, “Jensen’s inequality for operators without operator convexity,” Linear Algebra and its Applications, vol. 434, no. 5, pp. 1228-1237, 2011. · Zbl 1221.47032 · doi:10.1155/2011/358981 [5] Z. Pavić, “The applications of functional variants of Jensen’s inequality,” Journal of Function Spaces and Applications, vol. 2013, Article ID 194830, 5 pages, 2013. · Zbl 1300.46062 · doi:10.1155/2013/194830 [6] A. M. Mercer, “A variant of Jensen’s inequality,” Journal of Inequalities in Pure and Applied Mathematics, vol. 4, article 73, 2 pages, 2003. · Zbl 1048.26016 [7] T. Furuta, J. Mićić Hot, J. Pe, and Y. Seo, Mond-Pe Method in Operator Inequalities, vol. 1, Element, Zagreb, Croatia, 2005. · Zbl 1135.47012 [8] A. Matković, J. Pe, and I. Perić, “Refinements of Jensen’s inequality of Mercer’s type for operator convex functions,” Mathematical Inequalities & Applications, vol. 11, no. 1, pp. 113-126, 2008. · Zbl 1141.47013 · doi:10.7153/mia-11-07 [9] J. E. Pe, F. Proschan, and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, vol. 187, Academic Press, Boston, Mass, USA, 1992. · Zbl 0749.26004 [10] J. Mićić, Z. Pavić, and J. Pe, “The inequalities for quasiarithmetic means,” Abstract and Applied Analysis, vol. 2012, Article ID 203145, 25 pages, 2012. · Zbl 1246.26019 · doi:10.1155/2012/203145 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.