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On Jensen's Additive Inequality for Positive Convex Functions of Selfadjoint Operators in Hilbert Spaces

S. S. Dragomir

- Mathematics, College of Engineering and Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia


- School of Computer Science and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

Email address: sever.dragomir@vu.edu.au

Doi : https://doi.org/10.47013/13.4.8

Cited by : Jordan J. Math & Stat., 13 (4) (2020), 601 - 623


Received on: May 1, 2019;                                          Accepted on: Oct. 14, 2019

 Abstract. In this paper we obtain some additive refinements and reverses of Jensen’s inequality for positive convex/concave functions of selfadjoint operators in Hilbert spaces. Natural applications for power and exponential functions are provided.

Keywords: Young’s Inequality, Convex functions, Jensen’s inequality, Selfadjoint operator, Functions of selfadjoint operators.