The function [image omitted] for x > 0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function [image omitted] for a ∈ and t ∈ (0, ∞) is verified. The possible origin and background of the function (*) are revealed to be related to [image omitted] the remainder of Binet's formula. Some applications of above results to the difference of (x) are noted.
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Document Type: Research Article
Department of Mathematics, Sanmenxia Polytechnic, Sanmenxia City, Henan Province 472000, China
Department of Mathematics, Zhengzhou Teachers College, Zhengzhou City, Henan Province 450044, China
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China
Research Institute of Mathematical Inequality Theory, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China
Publication date: 2008-07-01
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