Abstract
In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen type and Jensen–Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen’s operator inequality for strongly convex functions. As a corollary, we improve the Hölder-McCarthy inequality under suitable conditions. More precisely we show that if \(Sp\left( A \right) \subset \left( 1,\infty \right) \), then
and if \(Sp\left( A \right) \subset \left( 0,1 \right) \), then
for each positive operator A and \(x\in \mathcal {H}\) with \(\left\| x \right\| =1\).
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Moradi, H.R., Omidvar, M.E., Adil Khan, M. et al. Around Jensen’s inequality for strongly convex functions. Aequat. Math. 92, 25–37 (2018). https://doi.org/10.1007/s00010-017-0496-5
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DOI: https://doi.org/10.1007/s00010-017-0496-5