有關具對數型凹函數正數列的不等式

On inequalities of positive and logarithmically convex sequences

李嘉修(Jia-shiou Li)

指導教授 ： 楊國勝

淡江大學/理學院/數學學系碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00056

摘要

在本文中我們推廣、整理了ㄧ些BAI-NI Gao 及 FENG QI所證明的不等式。

關鍵字

單調 ； 不等式 ； 幾何平均 ； 比率 ； 正序列 ； 對數型凸函數 ； 對數型凹函數 ； 數學歸納法

並列摘要

In the present note we established a generalization some of the inequalities that proof by BAI-NI Gao AND FENG QI.

並列關鍵字

monotonicity ； inequality ； geometric meam ； ratio ； positive sequence ； logarithmically concave ； logarithmically convex ； mathemathical induction

參考文獻

[1] BAI-NI Gao AND FENG QI, Monotonicity of sequences involving geometric means of positive sequences with monotonicity and logarithmical convexity, Mathematicity Inequalities & Applications, 9, 1 (2006). 1-9.

[2] H. ALZER, On an inequality of H. Minc and L. Sathre, J. Math. Anal.Appl., 179, (1993), 396-402.

[3] B.-N. Guo, F. QI, Inequalities and monotonicity for the ratio of gamma functions, Taiwanese J. Math., 7, 2 (2003), 239-247.

[7] J.-CH. KUANG, Some extensions and refinements of Minc-Sathre inequality, Math. Gaz., 83, (1999), 123-127.

[8] H. MINC, L. SATHRE, Some inequalities involving (r!)^{(1/r)}, Proc. Edinburgh Math. Soc., 14, (1964/65), 41-46.