共查询到20条相似文献,搜索用时 62 毫秒
1.
Briand et al. (Electron. Comm. Probab. 5 (2000) 101–117) gave a counterexample and proposition to show that given g,g-expectations usually do not satisfy Jensen's inequality for most of convex functions. This yields a natural question, under which conditions on g, do g-expectations satisfy Jensen's inequality for convex functions? In this paper, we shall deal with this question in the case that g is convex and give a necessary and sufficient condition on g under which Jensen's inequality holds for convex functions. To cite this article: Z. Chen et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
2.
Slavko Simic 《Journal of Mathematical Analysis and Applications》2008,343(1):414-419
In this paper we shall give a global upper bound for Jensen's inequality without restrictions on the target convex function f. We also introduce a characteristic c(f) i.e. an absolute constant depending only on f, by which the global bound is improved. 相似文献
3.
Soumyashant Nayak 《Journal of Functional Analysis》2018,274(10):2978-3002
A generalization of classical determinant inequalities like Hadamard's inequality and Fischer's inequality is studied. For a version of the inequalities originally proved by Arveson for positive operators in von Neumann algebras with a tracial state, we give a different proof. We also improve and generalize to the setting of finite von Neumann algebras, some ‘Fischer-type’ inequalities by Matic for determinants of perturbed positive-definite matrices. In the process, a conceptual framework is established for viewing these inequalities as manifestations of Jensen's inequality in conjunction with the theory of operator monotone and operator convex functions on . We place emphasis on documenting necessary and sufficient conditions for equality to hold. 相似文献
4.
Sheng Jun Fan 《数学学报(英文版)》2009,25(10):1681-1692
Under the Lipschitz assumption and square integrable assumption on g, Jiang proved that Jensen's inequality for BSDEs with generator g holds in general if and only if g is independent of y, g is super homogenous in z and g(t, 0) = 0, a.s., a.e.. In this paper, based on Jiang's results, under the same assumptions as Jiang's, we investigate the necessary and sufficient condition on g under which Jensen's inequality for BSDEs with generator g holds for some specific convex functions, which generalizes some known results on Jensen's inequality for BSDEs. 相似文献
5.
S. Leorato 《Journal of multivariate analysis》2009,100(5):1044-1060
Let f:X→R be a convex mapping and X a Hilbert space. In this paper we prove the following refinement of Jensen’s inequality:
E(f|X∈A)≥E(f|X∈B) 相似文献
6.
We give a matrix version of the scalar inequality f(a + b) ? f(a) + f(b) for positive concave functions f on [0, ∞). We show that Choi’s inequality for positive unital maps and operator convex functions remains valid for monotone convex functions at the cost of unitary congruences. Some inequalities for log-convex functions are presented and a new arithmetic-geometric mean inequality for positive matrices is given. We also point out a simple proof of the Bhatia-Kittaneh arithmetic-geometric mean inequality. 相似文献
7.
Kong-Ming Chong 《Journal of Mathematical Analysis and Applications》1976,56(2):309-316
This paper characterizes doubly stochastic operators between two L1 spaces of random variables in terms of convex functions on the real line. This characterization is then applied to proving some Hardy-Littlewood-Pólya-type rearrangement theorems. The conditional form of Jensen's inequality is also derived and a condition for equality obtained. Moreover, some known results concerning doubly stochastic operators are also generalized. 相似文献
8.
Let X(ω) be a random element taking values in a linear space endowed with the partial order ≤; let 0 be the class of nonnegative order-preserving functions on such that, for each g∈0, E[g(X)] is defined; and let 1?0 be the subclass of concave functions. A version of Markov's inequality for such spaces in P(X ≥ x) ≤ inf0E[g(X)]/g(x). Moreover, if E(X) = ξ is defined and if Jensen's inequality applies, we have a further inequality P(X≥x) ≤ inf1E[g(X)]/g(x) ≤ inf1g(ξ)/g(x). Applications are given using a variety or orderings of interest in statistics and applied probability. 相似文献
9.
Let (T,
, P) be a probability space,
a P-complete sub-δ-algebra of
and X a Banach space. Let multifunction t → Γ(t), t T, have a
(X)-measurable graph and closed convex subsets of X for values. If x(t) ε Γ(t) P-a.e. and y(·) ε Ep
x(·), then y(t) ε Γ(t) P-a.e. Conversely, x(t) ε F(Γ(t), y(t)) P-a.e., where F(Γ(t), y(t)) is the face of point y(t) in Γ(t). If X =
, then the same holds true if Γ(t) is Borel and convex, only. These results imply, in particular, extensions of Jensen's inequality for conditional expectations of random convex functions and provide a complete characterization of the cases when the equality holds in the extended Jensen inequality. 相似文献
10.
A normalized univalent function f is called Ma-Minda starlike or convex if zf′(z)/f(z)?φ(z) or 1+zf″(z)/f′(z)?φ(z) where φ is a convex univalent function with φ(0)=1. The class of Ma-Minda convex functions is shown to be closed under certain operators that are generalizations of previously studied operators. Analogous inclusion results are also obtained for subclasses of starlike and close-to-convex functions. Connections with various earlier works are made. 相似文献
11.
Christian Gros 《European Journal of Operational Research》1978,2(5):368-376
For a vector-valued function f, Sup f and Inf f are defined from the Yu's domination theory and the Pareto's efficiency. A notion of conjugate is proposed for convex vector-valued function, this construction gives once more the usual conjugate function: when the function f is scalar. Then, this concept is used to write the Fenchel's problem in convex multiple objective optimization and to prove the associated duality theorem. 相似文献
12.
E. A. Plotnikova 《Siberian Advances in Mathematics》2008,18(4):275-287
We obtain some integral representations of the form f(x) = P(f) + K(?f) on the Carnot groups, where P(f) is a polynomial and K is an integral operator with a specific singularity. These representations are employed to prove the weak Poincaré inequality. 相似文献
13.
We give some integral representations of the form f(x) = P(f)+K(?f) on two-step Carnot groups, where P(f) is a polynomial and K is an integral operator with a specific singularity. We then obtain the weak Poincaré inequality and coercive estimates as well as the generalized Poincaré inequality on the general Carnot groups. 相似文献
14.
W Stadje 《Journal of Mathematical Analysis and Applications》1984,102(1):149-155
A partial converse of Jensen's inequality for integrals of norms on k is proved. 相似文献
15.
Let G be a subset of a locally convex separated topological vector space E with int(G) ≠ Ø, cl(G) convex and quasi-complete. Let f: cl(G) → E be a continuous condensing multifunction with compact and convex values and with a bounded range. It is shown that for each w? int(G), there exists a u = u(w) ??(cl(G)) such that p(f(u) ? u) = inf{p(x ? y): x?f(u), y? cl(G)}, where p is the Minkowski's functional of the set (cl(G) ? w). Several fixed point results are obtained as a consequence of this result. 相似文献
16.
Imre Z Ruzsa 《Journal of Number Theory》1984,18(1):27-33
Elliott's generalization of the Turán-Kubilius inequality is further generalized by establishing an upper bound for the sum Σn≤xF(∣f(n) ? A∣), where f is a complex-valued additive arithmetical function, A an arbitrary number and F an arbitrary nonnegative-valued increasing function. A connected problem for group-valued functions is also considered. 相似文献
17.
Shijun Yang 《Applied Mathematics Letters》2012,25(3):571-574
Detailed analysis shows that a function f admits the double Jordan-type inequality if and only if f is analytic and even. Associated with f is the function g with f(x)=g(x2). In this short note, based on this association, and using properties of absolutely and/or (completely) monotonic functions, we propose a concise method to derive the inequality from the coefficients in the Taylor’s series of f. The results include some existing ones as special cases. 相似文献
18.
Jorge Antezana Demetrio Stojanoff 《Journal of Mathematical Analysis and Applications》2007,331(1):297-307
Let A be a C∗-algebra and be a positive unital map. Then, for a convex function defined on some open interval and a self-adjoint element a∈A whose spectrum lies in I, we obtain a Jensen's-type inequality f(?(a))??(f(a)) where ? denotes an operator preorder (usual order, spectral preorder, majorization) and depends on the class of convex functions considered, i.e., monotone convex or arbitrary convex functions. Some extensions of Jensen's-type inequalities to the multi-variable case are considered. 相似文献
19.
M. van den Berg 《Journal of Functional Analysis》2007,250(1):114-131
Upper bounds are obtained for the heat content of an open set D with singular initial condition f on a complete Riemannian manifold, provided (i) the Dirichlet-Laplace-Beltrami operator satisfies a strong Hardy inequality, and (ii) f satisfies an integrability condition. Precise asymptotic results for the heat content are obtained for an open bounded and connected set D in Euclidean space with C2 boundary, and with initial condition f(x)=δ(x)−α,0<α<2, where δ(x) is the distance from x to the boundary of D. 相似文献
20.
Let the process {Y(x,t) : t?T} be observable for each x in some compact set X. Assume that Y(x, t) = θ0f0(x)(t) + … + θkfk(x)(t) + N(t) where fi are continuous functions from X into the reproducing kernel Hilbert space H of the mean zero random process N. The optimum designs are characterized by an Elfving's theorem with the closed convex hull of the set {(φ, f(x))H : 6φ 6H ≤ 1, x?X}, where (·, ·)H is the inner product on H. It is shown that if X is convex and fi are linear the design points may be chosen from the extreme points of X. In some problems each linear functional c′θ can be optimally estimated by a design on one point x(c). These problems are completely characterized. An example is worked and some partial results on minimax designs are obtained. 相似文献