Results 21 to 30 of about 3,546,863 (46)
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 +3 more
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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
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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
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, 2011 A graph that admits a Smarandachely super mean m-labeling is called a Smarandachely super m-mean graph, particularly, a mean graph if m = 2. In this paper, some new families of mean graphs are investigated.
Vaidya, S.K.
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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
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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 +4 more
wiley +1 more source
Some Results on Super Mean Graphs [PDF]
, 2009 Approaching topics such as labeling, Smarandachely super mean labeling, Smarandachely super m-mean graph, super mean labeling, super mean ...
Nagarajan, A., Vasuki, R.
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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
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Optimal Lower Generalized Logarithmic Mean Bound for the Seiffert Mean
Journal of Applied Mathematics, Volume 2013, Issue 1, 2013., 2013 We present the greatest value p such that the inequality P(a, b) > Lp(a, b) holds for all a, b > 0 with a ≠ b, where P(a, b) and Lp(a, b) denote the Seiffert and pth generalized logarithmic means of a and b, respectively.
Ying-Qing Song +4 more
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Exact inequalities involving power mean, arithmetic mean and identric mean [PDF]
, 2011 For \(p\in \mathbb{R}\), the power mean \(M_{p}(a,b)\) of order \(p\), identric mean \(I(a,b)\) and arithmetic mean \(A(a,b)\) of two positive real numbers \(a\) and \(b\) are defined by \begin{equation*} M_{p}(a,b)= \begin{cases} \displaystyle\left(
Ming-yu Shi, Yue-ping Jiang, Yu-ming Chu
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