


Paper's Title:
A Double Inequality for Divided Differences and Some Identities of the Psi and Polygamma Functions
Author(s):
B. N. Guo and F. Qi
School of
Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan
Province, 454010, China
bai.ni.guo@gmail.com,
bai.ni.guo@hotmail.com
School of
Research Institute of Mathematical Inequality Theory, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China
qifeng618@gmail.com,
qifeng618@hotmail.com,
qifeng618@qq.com
URL:http://qifeng618.spaces.live.com
Abstract:
In this short note, from the logarithmically completely monotonic property of the function ^{ }, a double inequality for the divided differences and some identities of the psi and polygamma functions are presented.
Paper's Title:
A note on Inequalities due to Martins, Bennett and Alzer
Author(s):
József Sándor
BabeşBolyai University of Cluj, Department of Mathematics and Computer Sciences
Kogălniceanu Nr.1, ClujNapoca,
Romania.
jjsandor@hotmail.com
jsandor@member.ams.org
Abstract:
A short history of certain inequalities by Martins, Bennett as well as Alzer, is provided. It is shown that, the inequality of Alzer for negative powers [6], or Martin's reverse inequality [7] are due in fact to Alzer [2]. Some related results, as well as a conjecture, are stated.
Paper's Title:
Inequalities of Gamma Function Appearing in Generalizing Probability Sampling Design
Author(s):
Mohammadkheer M. AlJararha And Jehad M. AlJararha
Department of Mathematics,
Yarmouk University,
Irbid 21163,
Jordan.
Email: mohammad.ja@yu.edu.jo
Department of Statistics,
Yarmouk University,
Irbid 21163,
Jordan.
Email: jehad@yu.edu.jo
Abstract:
In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities can be used to generalize different probability distribution functions. Also, they can be used to generalize some statistical designs, e.g., the probability proportional to the size without replacement design.
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