1. G Hardy, J E Littlewood and G Pölya, Inequalities, Cambridge University Press, Second edition, 1952. (This is a well-known classic. Chapters II and III are devoted to ‘mean values’.)
2. P S Bullen, D S Mitrinovic and P M Vasic, Means and their Inequalities, D Reidel, 1998. (A specialised monograph devoted exclusively to various means.)
3. W H McAdams, Heat Transmission, Third edition, McGraw Hill, 1954. (An engineering text in which the logarithmic mean is introduced in the context of fluid flow.)
4. B C Carlson, The logarithmic mean, American Mathematical Monthly, Vol.79,pp.615–618, 1972. (A very interesting article from which we have taken some of the material presented here.)
5. R Bhatia, Positive Definite Matrices, Princeton Series in Applied Mathematics, 2007, and also TRIM 44, Hindustan Book Agency, 2007. (Matrix versions of means, and inequalities for them, can be found here. The role of the logarithmic mean in this context is especially emphasized in Chapters 4–6.)