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Order generalised gradient and operator inequalities

Dragomir, Sever S ORCID: 0000-0003-2902-6805 and Kikianty, E (2015) Order generalised gradient and operator inequalities. Journal of Inequalities and Applications, 2015 (1). ISSN 1025-5834

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Abstract

We introduce the notion of order generalised gradient, a generalisation of the notion of subgradient, in the context of operator-valued functions. We state some operator inequalities of Hermite-Hadamard and Jensen types. We discuss the connection between the notion of order generalised gradient and the Gâteaux derivative of operator-valued functions. We state a characterisation of operator convexity via an inequality concerning the order generalised gradient.

Item Type: Article
Uncontrolled Keywords: subgradient inequality; operator convex function; operator inequality
Subjects: FOR Classification > 0102 Applied Mathematics
Faculty/School/Research Centre/Department > College of Science and Engineering
Depositing User: Symplectic Elements
Date Deposited: 13 Sep 2016 04:05
Last Modified: 20 Aug 2019 01:15
URI: http://vuir.vu.edu.au/id/eprint/31545
DOI: https://doi.org/10.1186/s13660-015-0574-y
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Citations in Scopus: 0 - View on Scopus

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