Results 21 to 30 of about 226 (67)

Logarithmic convexity of Gini means [PDF]

Jiao-Lian Zhao, Qiu-Ming Luo, Bai-Ni Guo, and Feng Qi, Logarithmic convexity of Gini means, Journal of Mathematical Inequalities 6 (2012), no. 4, 509--516, 2009
In the paper, the monotonicity and logarithmic convexity of Gini means and related functions are investigated.
arxiv   +1 more source

Monotonicity results and bounds for the inverse hyperbolic sine [PDF]

Bai-Ni Guo, Qiu-Ming Luo, and Feng Qi, Monotonicity results and inequalities for the inverse hyperbolic sine function, Journal of Inequalities and Applications 2013, 2013:536, 6 pages, 2009
In this note, we present monotonicity results of a function involving to the inverse hyperbolic sine. From these, we derive some inequalities for bounding the inverse hyperbolic sine.
arxiv   +1 more source

Monotonicity properties and inequalities related to generalized Grötzsch ring functions

Open Mathematics, 2019
In the paper, the authors present some monotonicity properties and some sharp inequalities for the generalized Grötzsch ring function and related elementary functions. Consequently, the authors obtain new bounds for solutions of the Ramanujan generalized
Wang Fei, He Jian-Hui, Yin Li, Qi Feng
doaj   +1 more source

Two monotonic functions involving gamma function and volume of unit ball [PDF]

Bai-Ni Guo and Feng Qi, Monotonicity of functions connected with the gamma function and the volume of the unit ball, Integral Transforms and Special Functions 23 (2012), no. 9, 701--708, 2010
In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.
arxiv   +1 more source

An inequality involving the gamma and digamma functions [PDF]

Journal of Applied Analysis 22 (2016), no. 1, 49--54, 2011
In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.
arxiv   +1 more source

Complete monotonicity of a function involving the gamma function and applications [PDF]

Periodica Mathematica Hungarica 69 (2014), no. 2, 159--169, 2011
In the article we present necessary and sufficient conditions for a function involving the logarithm of the gamma function to be completely monotonic and apply these results to bound the gamma function $\Gamma(x)$, the $n$-th harmonic number $\sum_{k=1}^n\frac1k$, and the factorial $n!$.
arxiv   +1 more source

Characterizations of minimal elements of upper support with applications in minimizing DC functions

Open Mathematics
In this study, we discuss on the problem of minimizing the differences of two non-positive valued increasing, co-radiant and quasi-concave (ICRQC) functions defined on XX (where XX is a real locally convex topological vector space).
Mirzadeh Somayeh, Barsam Hasan, Ciurdariu Loredana   +2 more
doaj   +1 more source

Properties of three functions relating to the exponential function and the existence of partitions of unity [PDF]

International Journal of Open Problems in Computer Science and Mathematics 5 (2012), no. 3, 122--127, 2012
In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete monotonicity, logarithmically complete monotonicity, absolute monotonicity, and the like.
arxiv   +1 more source

Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function

Demonstratio Mathematica
In this study, using convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other analytic techniques, the authors verify decreasing property
Yin Hong-Ping, Han Ling-Xiong, Qi Feng
doaj   +1 more source

Integral representation of some functions related to the Gamma function [PDF]

arXiv, 2004
We prove that the functions Phi(x)=[Gamma(x+1)]^{1/x}(1+1/x)^x/x and log Phi(x) are Stieltjes transforms.
arxiv