共查询到20条相似文献,搜索用时 15 毫秒
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Qian Zhang 《Journal of Mathematical Analysis and Applications》2011,379(1):65-74
In this paper, we study the invariance of the geometric mean with respect to some generalized quasi-arithmetic means, namely, we present some results concerning the functional equation
3.
Let (GA)
n
[k](a), A
n
(a), G
n
(a) be the third symmetric mean of k degree, the arithmetic and geometric means of a
1, …, a
n
(a
i
> 0, i = 1, …, n), respectively. By means of descending dimension method, we prove that the maximum of p is k−1/n−1 and the minimum of q is n/n−1(k−1/k)
k/n
so that the inequalities {fx505-1} hold. 相似文献
4.
Chao-Ping Chen 《Journal of Mathematical Analysis and Applications》2008,345(1):86-89
A monotonicity result for the ratio between two generalized logarithmic means is established. As an application, an inequality of Alzer for negative powers is extended to all real numbers. 相似文献
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Dorota G?azowska Janusz Matkowski 《Journal of Mathematical Analysis and Applications》2007,331(2):1187-1199
The invariance of the geometric mean G with respect to the Lagrangian mean-type mapping (Lf,Lg), i.e. the equation G○(Lf,Lg)=G, is considered. We show that the functions f and g must be of high class regularity. This fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g. 相似文献
6.
We give a characterization for the geometric mean inequality to hold for the case 0 < q < p ≤ ∞, p > 1, where f is positive a.e. on (0, ∞), and C > 0 independent of f. 相似文献
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Feng Qi Senlin Guo Shou-Xin Chen 《Journal of Computational and Applied Mathematics》2008,220(1-2):111-118
In the paper, a new upper bound in the second Kershaw's double inequality involving ratio of gamma functions is established, and, as generalizations of the second Kershaw's double inequality, the divided differences of the psi and polygamma functions are bounded. 相似文献
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Richard E. Pfiefer 《Journal of Theoretical Probability》1990,3(2):169-179
Ifv
r is ther-dimensional volume of ther-simplex formed byr+1 points taken at random from a compact setK in
n
, withrn, andh is a (strictly) increasing function, then the (unique) compact set that gives the minimum expected value ofh o v
r, is proved to be the ellipsoid (whenr=n) and the ball (whenr) almost everywhere. This result is established by using a single integral inequality for centrally symmetric quasiconvex functions integrated over compact rectangles. 相似文献
9.
J. Sándor 《Aequationes Mathematicae》1990,40(1):261-270
Summary Leta, b > 0 be positive real numbers. The identric meanI(a, b) of a andb is defined byI = I(a, b) = (1/e)(b
b
/a
a
)
1/(b–a)
, fora b, I(a, a) = a; while the logarithmic meanL(a, b) ofa andb isL = L(a, b) = (b – a)/(logb – loga), fora b, L(a, a) = a. Let us denote the arithmetic mean ofa andb byA = A(a, b) = (a + b)/2 and the geometric mean byG =G(a, b) =
. In this paper we obtain some improvements of known results and new inequalities containing the identric and logarithmic means. The material is divided into six parts. Section 1 contains a review of the most important results which are known for the above means. In Section 2 we prove an inequality which leads to some improvements of known inequalities. Section 3 gives an application of monotonic functions having a logarithmically convex (or concave) inverse function. Section 4 works with the logarithm ofI(a, b), while Section 5 is based on the integral representation of means and related integral inequalities. Finally, Section 6 suggests a new mean and certain generalizations of the identric and logarithmic means. 相似文献
10.
If M is a mean on and M(f(x1),f(x2),…,f(xn))=f(M(x1,x2,…,xn)) then we say that M is invariant under f. The problem is to find a class of functions that by invariance determines a mean uniquely. We focus on the geometric mean, which can be transformed to obtain results for other means. 相似文献
11.
Pedro Ortega Salvador Consuelo Ramírez Torreblanca 《Journal of Mathematical Analysis and Applications》2007,336(1):593-607
We characterize the pairs of weights (u,v) such that the geometric mean operator G1, defined for positive functions f on (0,∞) by
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For n positive definite operators A1,…,An, Ando-Li-Mathias defined geometric mean of n-operators by symmetric procedure. It has many nice properties, and is studied by many authors. But the process is so complicated to compute. In this paper, we shall attempt to make a new construction of geometric mean of n-operators which we can compute it easier than geometric mean by Ando–Li–Mathias. 相似文献
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In this paper, we introduce an inequality for distances between every two points among the given 2n points and apply this inequality to a partial solution of the Aleksandrov-Rassias problem, which was first posed by Th.M. Rassias. 相似文献
14.
Masayuki Fujimoto 《Linear and Multilinear Algebra》2018,66(8):1564-1577
In this paper, by virtue of the matrix geometric mean and the polar decomposition, we present new Wielandt type inequalities for matrices of any size. To this end, based on results due to J.I. Fujii, we reform a matrix Cauchy–Schwarz inequality, which differs from ones due to Marshall and Olkin. As an application, we show a new block matrix version of Wielandt type inequalities under the block rank additivity condition. 相似文献
15.
Masamitsu Ohnishi 《Mathematical and Computer Modelling》2003,38(11-13):1381
This paper examines an optimal stopping problem for a geometric Brownian motion with random jumps. It is assumed that jumps occur according to a time-homogeneous Poisson process and the proportions of these sizes are independent and identically distributed nonpositive random variables. The objective is to find an optimal stopping time of maximizing the expected discounted terminal reward which is defined as a nondecreasing power function of the stopped state. By applying the “smooth pasting technique” [1,2], we derive almost explicitly an optimal stopping rule of a threshold type and the optimal value function of the initial state. That is, we express the critical state of the optimal stopping region and the optimal value function by formulae which include only given problem parameters except an unknown to be uniquely determined by a nonlinear equation. 相似文献
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Koenraad M.R. Audenaert 《Linear algebra and its applications》2007,422(1):279-283
We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by Zhan. 相似文献
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We obtain eigenvalue inequalities for matrix geometric means of positive definite matrices. This implies matrix norm inequalities for unitarily invariant norms, which are considered as complementary to a series of norm inequalities among geometric means. We give complements of the Ando–Hiai type inequality for the Karcher mean by means of the generalized Kantorovich constant. Finally, we consider the monotonicity of the eigenvalue function for the Karcher mean. 相似文献
19.
For a Riemannian closed spin manifold and under some topological assumption (non-zero A-genus or enlargeability in the sense of Gromov-Lawson), we give an optimal upper bound for the infimum of the scalar curvature in terms of the first eigenvalue of the Laplacian. The main difficulty lies in the study of the odd-dimensional case. On the other hand, we study the equality case for the closed spin Riemannian manifolds with non-zero A-genus. This work improves an inequality which was first proved by K. Ono in 1988.
Mathematics Subject Classification (2000):58J50, 35P15, 46L10, 58G11. 相似文献
20.
Shanhe Wu 《Journal of Mathematical Analysis and Applications》2005,312(2):637-652
In this paper, we generalize and sharpen the power means inequality by using the theory of majorization and the analytic techniques. Our results unify some optimal versions of the power means inequality. As application, a well-known conjectured inequality proposed by Janous et al. is proven. Furthermore, these results are used for studying a class of geometric inequalities for simplex, from which, some interesting inequalities including the refined Euler inequality and the reversed Finsler-Hadwiger type inequality are obtained. 相似文献