... Publishing CorporationJournal of Inequalities and ApplicationsVolume 2008, Article ID 870950, 4 pagesdoi:10.1155/2008/870950 Research Article On Logarithmic Convexity for Ky-Fan InequalityMatloob ... well known that Ky-Fan inequality can be obtained from the Levinson inequality 1, seealso 2, page 71.Theorem 1.1. Let f be a real-valued 3-convex function on 0, 2a,thenfor0 <xi<a, ... R,ξsξt≥ ξ2r ξ2st/2, 2.3that is, ξsis log convex in the Jensen sense;2 ξsis continuous on I ⊆ R,itisalsolog convex, that is, for r<s<t,ξt−rs≤ ξt−srξs−rt2.4withξ012lnGanAnGnAan,...