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A class of completely mixed monotonic functions involving the gamma function with applications


Authors: Zhen-Hang Yang and Jing-Feng Tian
Journal: Proc. Amer. Math. Soc. 146 (2018), 4707-4721
MSC (2010): Primary 33B15, 26B25; Secondary 26D15
DOI: https://doi.org/10.1090/proc/14199
Published electronically: August 10, 2018
MathSciNet review: 3856139
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Abstract: In this paper, we introduce the notion of completely mixed monotonicity of a function of several variables, very few of which have appeared. We give a necessary and sufficient condition for a function constructed by ratios of gamma functions to be completely mixed monotonic. From this, some new inequalities for gamma, psi, and polygamma functions are derived.


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Additional Information

Zhen-Hang Yang
Affiliation: College of Science and Technology, North China Electric Power University, Baoding, Hebei Province, 071051, People’s Republic of China — and — Department of Science and Technology, State Grid Zhejiang Electric Power Company Research Institute, Hangzhou, Zhejiang, 310014, People’s Republic of China
Email: yzhkm@163.com

Jing-Feng Tian
Affiliation: College of Science and Technology, North China Electric Power University, Baoding, Hebei Province, 071051, People’s Republic of China
Email: tianjf@ncepu.edu.cn

DOI: https://doi.org/10.1090/proc/14199
Keywords: Completely mixed monotonic function, gamma function, psi function, polygamma function, inequality
Received by editor(s): January 2, 2018
Published electronically: August 10, 2018
Additional Notes: The second author is the corresponding author.
Communicated by: Mourad Ismail
Article copyright: © Copyright 2018 American Mathematical Society