Generalizations of Alzer's and Kuang's inequality

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Feng Qi


Let $ f$ be a strictly increasing convex (or concave) functions on $ (0,1]$, then, for $ k$ being a nonnegative integer and $ n$ a natural number, the sequence $ {1\over n}\sum_{i=k+1}^{n+k} f({i\over n+k})$ is decreasing in $ n$ and $ k$ and has a lower bound $ \int_0^1 f(t) dt$. Form this, some new inequalities involving $ {\root n\of {(n+k)!/k!}}$ are deduced. By the Hermie-Hadamard inequality, several inequalities are obtained.

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How to Cite
Qi, F. (2000). Generalizations of Alzer’s and Kuang’s inequality. Tamkang Journal of Mathematics, 31(3), 223–228.
Author Biography

Feng Qi

Department of Mathematics, Jiaozuo Institute of Technology, #142, Mid-Jiefang Road, Jiaozuo City, Henan 454000, china.

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