Mathematics – Classical Analysis and ODEs
Scientific paper
2009-03-29
Bai-Ni Guo and Feng Qi, University Politehnica of Bucharest Scientific Bulletin Series A---Applied Mathematics and Physics 72
Mathematics
Classical Analysis and ODEs
8 pages
Scientific paper
In the article, a notion "logarithmically absolutely monotonic function" is introduced, an inclusion that a logarithmically absolutely monotonic function is also absolutely monotonic is revealed, the logarithmically complete monotonicity and the logarithmically absolute monotonicity of the function $\bigl(1+\frac{\alpha}x\bigr) ^{x+\beta}$ are proved, where $\alpha$ and $\beta$ are given real parameters, a new proof for the inclusion that a logarithmically completely monotonic function is also completely monotonic is given, and an open problem is posed.
Guo Bai-Ni
Qi Feng
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