05904390

j

05904390 Dragomir, S.S. Inequalities in terms of the G\^ateaux derivatives for convex functions on linear spaces with applications. Bull. Aust. Math. Soc. 83, No. 3, 500-517 (2011). 2011 Cambridge University Press, Cambridge EN convex function Gateaux derivatives Jensen's inequality norm mean f-deviations f-divergence

doi:10.1017/S0004972710002054

Motivated by some published refinement results and using techniques from real analysis, a refinement and a reverse of Jensen's inequality for convex functions defined on linear spaces in terms of the Gateaux derivatives are derived. Applications for norms, bounds for the mean f-derivations and f-divergence measures are provided as well. Bicheng Yang (Guangdong)