Hermite–Hadamard type inequalities for operator geometrically convex functions
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In this paper, we introduce the concept of operator geometrically convex functions for positive linear operators and prove some Hermite–Hadamard type inequalities for these functions. As applications, we obtain trace inequalities for operators which give some refinements of previous results.
KeywordsHermite–Hadamard inequality Operator geometrically convex function Trace inequality Unitarily invariant norm
Mathematics Subject Classification47A63 15A60 47B05 47B10 26D15
This work was written whilst the second author was visiting Victoria University during his short sabbatical leave provided by the Ministry of Science, Research and Technology. He thanks them for the support and hospitality.
- 3.Dannan, F.M.: Matrix and operator inequalities. J. Inequal. Pure Appl. Math. 2 (2001) (article 34)Google Scholar
- 5.Dragomir, S.S.: Some inequalities for trace class operators via a Kato’s result. RGMIA Res. Rep. Coll. 17 (2014) (preprint, article 105)Google Scholar
- 7.İscan, İ.: Some new Hermite–Hadamard type inequalities for geometrically convex functions. Math. Stat. 1, 86–91 (2013)Google Scholar
- 8.İscan, İ.: On some new Hermite–Hadamard type inequalities for \(s\)-geometrically convex functions. Int. J. Math. Math. Sci. 2014 (2014) (article ID 163901, 8 pages)Google Scholar
- 15.Taghavi, A., Darvish, V., Nazari, H.M., Dragomir, S.S.: Some inequalities associated with the Hermite–Hadamard inequalities for operator \(h\)-convex functions. RGMIA Research Report Collection, vol. 18 (2015) (article 22)Google Scholar
- 17.Zhu, K.: An Introduction to Operator Algebras. CRC Press, Boca Raton (1993)Google Scholar