For with , the Schwab-Borchardt mean is defined as . In this paper, we find the greatest values of and and the least values of and in such that and . Similarly, we also find the greatest values of and and the least values of and in such that and . Here, , , and are the harmonic, arithmetic, and contraharmonic means, respectively, and , , , and are four Neuman means derived from the Schwab-Borchardt mean.
"Optimal Bounds for Neuman Means in Terms of Harmonic and Contraharmonic Means." J. Appl. Math. 2013 1 - 4, 2013. https://doi.org/10.1155/2013/807623