Geodesic
Inequalities involving operator superquadratic functions
Filomat, Tome 35 (2021) no. 9, p. 3151

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DOI

In this paper, related to the well-known operator convex functions, we study a class of operator functions, the operator superquadratic functions. We present some Jensen-type operator inequalities for these functions. In particular, we show that f : [0, ∞) → R is an operator midpoint superquadratic function if and only if f (C * AC) ≤ C * f (A)C − f C * A 2 C − (C * AC) 2 holds for every positive operator A ∈ B(H) + and every contraction C. As applications, some inequalities for quasi-arithmetic operator means are given
DOI : 10.2298/FIL2109151M
Classification : 47A63, 47A64
Keywords: operator inequality, operator superquadratic function, operator convex function, Jensen operator inequality, quasi- arithmetic operator mean 
Jadranka Mićić; Mohsen Kian. Inequalities involving operator superquadratic functions. Filomat, Tome 35 (2021) no. 9, p. 3151 . doi: 10.2298/FIL2109151M
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     title = {Inequalities involving operator superquadratic functions},
     journal = {Filomat},
     pages = {3151 },
     year = {2021},
     volume = {35},
     number = {9},
     doi = {10.2298/FIL2109151M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2109151M/}
}
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