Abstract
In this paper, we introduce the concept of operator geometrically convex functions for positive linear operators and prove some Hermite–Hadamard type inequalities for these functions. As applications, we obtain trace inequalities for operators which give some refinements of previous results.
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Acknowledgments
This work was written whilst the second author was visiting Victoria University during his short sabbatical leave provided by the Ministry of Science, Research and Technology. He thanks them for the support and hospitality.
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Communicated by A. Constantin.
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Taghavi, A., Darvish, V., Nazari, H.M. et al. Hermite–Hadamard type inequalities for operator geometrically convex functions. Monatsh Math 181, 187–203 (2016). https://doi.org/10.1007/s00605-015-0816-6
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DOI: https://doi.org/10.1007/s00605-015-0816-6
Keywords
- Hermite–Hadamard inequality
- Operator geometrically convex function
- Trace inequality
- Unitarily invariant norm