Results 31 to 40 of about 129 (75)

A Sharp Lower Bound for Toader‐Qi Mean with Applications

Journal of Function Spaces, Volume 2016, Issue 1, 2016., 2016
We prove that the inequality TQ(a, b) > Lp(a, b) holds for all a, b > 0 with a ≠ b if and only if p ≤ 3/2, where TQ(a,b)=2/π∫0π/2acos2θbsin2θdθ, Lp(a, b) = [(bp − ap)/(p(b − a))] 1/p (p ≠ 0), and L0(a,b)=ab are, respectively, the Toader‐Qi and p‐order logarithmic means of a and b.
Zhen-Hang Yang, Yu-Ming Chu, Kehe Zhu
wiley   +1 more source

Best Possible Bounds for Yang Mean Using Generalized Logarithmic Mean

Mathematical Problems in Engineering, Volume 2016, Issue 1, 2016., 2016
We prove that the double inequality Lp(a, b) < U(a, b) < Lq(a, b) holds for all a, b > 0 with a ≠ b if and only if p ≤ p0 and q ≥ 2 and find several sharp inequalities involving the trigonometric, hyperbolic, and inverse trigonometric functions, where p0 = 0.5451⋯ is the unique solution of the equation (p+12) 1/p=2π/ on the interval (0, ∞), U(a,b)=(a-b)
Wei-Mao Qian, Yu-Ming Chu, Kishin Sadarangani   +2 more
wiley   +1 more source

Sharp Power Mean Bounds for the One‐Parameter Harmonic Mean

Journal of Function Spaces, Volume 2015, Issue 1, 2015., 2015
We present the best possible parameters α = α(r) and β = β(r) such that the double inequality Mα(a, b) < Hr(a, b) < Mβ(a, b) holds for all r ∈ (0, 1/2) and a, b > 0 with a ≠ b, where Mp(a, b) = [(ap + bp)/2] 1/p (p ≠ 0) and M0(a, b)=ab and Hr(a, b) = 2[ra + (1 − r)b][rb + (1 − r)a]/(a + b) are the power and one‐parameter harmonic means of a and b ...
Yu-Ming Chu, Li-Min Wu, Ying-Qing Song, David R. Larson   +3 more
wiley   +1 more source

A Survey on Operator Monotonicity, Operator Convexity, and Operator Means

International Journal of Analysis, Volume 2015, Issue 1, 2015., 2015
This paper is an expository devoted to an important class of real‐valued functions introduced by Löwner, namely, operator monotone functions. This concept is closely related to operator convex/concave functions. Various characterizations for such functions are given from the viewpoint of differential analysis in terms of matrix of divided differences ...
Pattrawut Chansangiam, Julien Salomon
wiley   +1 more source

Hermite‐Hadamard and Simpson‐Like Type Inequalities for Differentiable Harmonically Convex Functions

Journal of Mathematics, Volume 2014, Issue 1, 2014., 2014
A new identity for differentiable functions is derived. A consequence of the identity is that the author establishes some new general inequalities containing all of the Hermite‐Hadamard and Simpson‐like types for functions whose derivatives in absolute value at certain power are harmonically convex.
İmdat İşcan, Roberto A. Kraenkel
wiley   +1 more source

New General Integral Inequalities for Lipschitzian Functions via Hadamard Fractional Integrals

International Journal of Analysis, Volume 2014, Issue 1, 2014., 2014
The author obtains new estimates on generalization of Hadamard, Ostrowski, and Simpson type inequalities for Lipschitzian functions via Hadamard fractional integrals. Some applications to special means of positive real numbers are also given.
İmdat İşcan, Julien Salomon
wiley   +1 more source

Sharp Inequalities for Trigonometric Functions

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
We establish several sharp inequalities for trigonometric functions and present their corresponding inequalities for bivariate means.
Zhen-Hang Yang, Yun-Liang Jiang, Ying-Qing Song, Yu-Ming Chu, Chun-Gang Zhu   +4 more
wiley   +1 more source

A Class of Logarithmically Completely Monotonic Functions and Their Applications

Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014
We study the recent investigations on a class of functions which are logarithmically completely monotonic. Two open problems are also presented.
Senlin Guo, Qiu-Ming Luo
wiley   +1 more source

Integral Representations for Bivariate Complex Geometric Mean and Applications

, 2017
In the paper, the authors survey integral representations (including the L&eacute;vy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the ...
Feng Qi, Dongkyu Lim
core   +1 more source