Jensen–Mercer Operator Inequalities Involving Superquadratic Functions
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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.
KeywordsSuperquadratic function Operator inequality Jensen–Mercer operator inequality operator order Ky Fan–Furuta constant
Mathematics Subject ClassificationPrimary 47A63 Secondary 15A60
The author would like to thank the referee for the helpful comments and suggestions to improve the paper.
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