Jensen–Mercer Operator Inequalities Involving Superquadratic Functions

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Abstract

A variant of the Jensen–Mercer operator inequality is proved for a superquadratic function and positive linear operators on a Hilbert space using a theorem of Neumark. Moreover, function order preserving operator inequalities for superquadratic functions is established. As application, a Kantorovich-type order preserving operator inequality via the Ky Fan–Furuta constant is obtained.

Keywords

Superquadratic function Operator inequality Jensen–Mercer operator inequality operator order Ky Fan–Furuta constant 

Mathematics Subject Classification

Primary 47A63 Secondary 15A60 

Notes

Acknowledgements

The author would like to thank the referee for the helpful comments and suggestions to improve the paper.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of NeyshaburNeyshaburIran

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