Order generalised gradient and operator inequalities

Journal of inequalities and applications

Sever S Dragomir¹ 

关键词: subgradient inequality;    operator convex function;    operator inequality;    47A63;    46E40;   

DOI  :  10.1186/s13660-015-0574-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY