Order generalised gradient and operator inequalities

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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

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.

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Item type Article
URI https://vuir.vu.edu.au/id/eprint/31545
DOI 10.1186/s13660-015-0574-y
Official URL https://journalofinequalitiesandapplications.sprin...
Subjects Historical > FOR Classification > 0102 Applied Mathematics
Current > Division/Research > College of Science and Engineering
Keywords subgradient inequality; operator convex function; operator inequality
Citations in Scopus 1 - View on Scopus
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