Abstract
Sharp companion inequalities for certain bivariate means are obtained. In particular, companion inequalities for those discovered by Stolarsky and S?ndor are established.
Highlights
The logarithmic and identric means of two positive numbers a and b are defined by (1) L ≡ L(a, b) = log a, b b − − a log a, a=b a=b and (2) 1/(b−a), a=b a = b, respectively
We will give a new proof of this result which shows that the associated constants are optimal
A companion inequality to (8) is contained in the following
Summary
Sharp companion inequalities for certain bivariate means are obtained. Companion inequalities for those discovered by Stolarsky and Sandor are established. The logarithmic and identric means of two positive numbers a and b are defined by Many remarkable inequalities and identities have been established.
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