... anonymous referee for many valuable comments, for acorrection of one part of the proof, and for his improving of the organization of the paper.This work was supported by Vega no. 1/0157/08 and Kega ... b,andpα is the best constant.Hindawi Publishing CorporationJournal of Inequalities and ApplicationsVolume 2010, Article ID 902432, 5 pagesdoi:10.1155/2010/902432 Research Article Proof of ... b1.3holds for α ∈ 1/2, 1 and all a, b > 0witha/ b? For information on the history, background, properties, and applications of inequali-ties for generalized logarithmic, arithmetic, and geometric...