Results 31 to 40 of about 3,756,040 (69)

Sharp One‐Parameter Mean Bounds for Yang Mean

Mathematical Problems in Engineering, Volume 2016, Issue 1, 2016., 2016
We prove that the double inequality Jα(a, b) < U(a, b) < Jβ(a, b) holds for all a, b > 0 with a ≠ b if and only if α≤2/(π-2)=0.8187⋯ and β ≥ 3/2, where U(a,b)=(a-b)/[2arctan⁡((a-b)/2ab)], and Jp(a, b) = p(ap+1 − bp+1)/[(p + 1)(ap − bp)] (p ≠ 0, −1), J0(a, b) = (a − b)/(log⁡a − log⁡b), and J−1(a, b) = ab(log⁡a − log⁡b)/(a − b) are the Yang and pth one ...
Wei-Mao Qian, Yu-Ming Chu, Xiao-Hui Zhang, Yann Favennec   +3 more
wiley   +1 more source

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

Inequalities of Hadamard's Type for Lipschitzian Mappings and their Applications [PDF]

, 1999
In this paper, we give some inequalities of Hadamard's type for M-Lipschitzian functions. Some applications which are connected with arithmetic mean, geometric mean, harmonic mean, logarithmical mean, identric mean, etc,.
Dragomir, Sever S, Kim, Seong Sik, Cho, Yeol Je   +2 more
core   +3 more sources

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

An Inequality of Grüss Type for Riemann-Stieltjes Integral and Applications for Special Means [PDF]

, 1998
In this paper we derive a new inequality of Grüss' type for Riemann-Stieltjes integral and apply it for special means (logarithmic mean, identric mean, etc...)
Fedotov, I, Dragomir, Sever S
core   +3 more sources

On Certain Inequalities for Means, III

, 1999
A sequential method is applied to obtain inequalities between a mean introduced by H.-J. Seiffert [9], and other means, including the logarithmic mean, the identric mean and the arithmetic-geometric mean of ...
Sándor, József
core   +3 more sources

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