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More about Jensen's inequality and Cauchy's means for superquadratic functions (CROSBI ID 196919)
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Abramovich, Shoshana ; Farid, G. ; Pečarić, Josip
More about Jensen's inequality and Cauchy's means for superquadratic functions // Journal of mathematical inequalities, 7 (2013), 1; 11-14. doi: 10.7153/jmi-07-02
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Abramovich, Shoshana ; Farid, G. ; Pečarić, Josip
engleski
More about Jensen's inequality and Cauchy's means for superquadratic functions
One of the many inequalities that superquadratic functions satisfy is the parallelogram inequality f(u+v)+f(u-v)>= 2f(u)+2f(v). In this paper, we present Cauchy means for superquadratic functions and other mean value theorems. We show also positive semi-definiteness, log-convexity, exponential convexity of certain set of functions.
Jensen’s inequality; log-convex function; linear functional; superquadracity; mean value theorems
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