Optimal Lehmer Mean Bounds for the Combinations of Identric and Logarithmic Means

Abstract EN

For any α∈0,1, we answer the questions: what are the greatest values p and λ and the least values q and μ, such that the inequalities Lpa,b0 with a≠b? Here, Ia,b, La,b, and Lpa,b denote the identric, logarithmic, and pth Lehmer means of two positive numbers a and b, respectively.