Multidimensional Jensen's operator on a Hilbert space and applications (CROSBI ID 176716)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Krnić, Mario ; Lovričević, Neda ; Pečarić, Josip
engleski
Multidimensional Jensen's operator on a Hilbert space and applications
Motivated by a joint concavity of connections, solidarities and multidimensional weighted geometric mean, in this paper we extend an idea of convexity (concavity) to operator functions of several variables. With the help of established definitions, we introduce the so called multidimensional Jensen's operator and study its properties. In such a way we get the lower and upper bounds for the above mentioned operator, expressed in the terms of the non-weighted operator of the same type. As an application, we obtain both refinements and converses for operator variants of some well known classical inequalities. In order to obtain the refinements of Jensen's integral inequality, we also consider an integral analogue of Jensen's operator for functions of one variable.
Jensen's operator inequality; operator convexity; operator concavity; multidimensional Jensen's operator; Jensen's integral operator; connection; solidarity; the relative operator entropy; multidimensional weighted geometric mean
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Podaci o izdanju
436 (7)
2012.
2583-2596
objavljeno
0024-3795
10.1016/j.laa.2011.09.013