We answer the question: for with , what are the greatest value and the least value , such that the double inequality holds for all with ? Here , , , and denote the generalized logarithmic, arithmetic, geometric, and harmonic means of two positive numbers and , respectively.
Yu-Ming Chu. Bo-Yong Long. "Best Possible Inequalities between Generalized Logarithmic Mean and Classical Means." Abstr. Appl. Anal. 2010 1 - 13, 2010. https://doi.org/10.1155/2010/303286