On the Monotonicity of √(Hf(p,q)Hf(-p,q)) and its Applications

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Yang, Zhenhang (2006) On the Monotonicity of √(Hf(p,q)Hf(-p,q)) and its Applications. Research report collection, 9 (2).


Let f(x, y) be a positive symmetric n-order homogenous function defined on R₊xR₊ which is three-time differentiable. Then √(Hf(p,q)Hf(-p,q)) is strictly increasing (decreasing) in p on (0,∞) if J = (x − y)(xI)x < (>)0, where I = (ln f)xy. As applications, H. Alzer’s inequalities are generalized and refined, some new inequalities for logarithmic mean, arithmetic mean and exponential mean are presented.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/18237
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords two-parameter homogeneous functions, monotonicity, inequality, mean
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