共查询到20条相似文献,搜索用时 657 毫秒
1.
We show that if T:X→X is a continuous linear operator on an F-space X≠{0}, then the set of frequently hypercyclic vectors of T is of first category in X, and this answers a question of A. Bonilla and K.-G. Grosse-Erdmann. We also show that if T:X→X is a bounded linear operator on a Banach space X≠{0} and if T is frequently hypercyclic (or, more generally, syndetically transitive), then the T∗-orbit of every non-zero element of X∗ is bounded away from 0, and in particular T∗ is not hypercyclic. 相似文献
2.
Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are Lipschitz ?-strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
3.
Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are bounded strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. A new explicit coupled iteration process is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
4.
Let C be a nonempty subset of a topological vector space E. We state and prove new various fixed point theorems of Fan–Browder type for set-valued maps F:C→2E such that C⊂F(C) (called expansive), without assuming that the sets C and F(C) are convex or compact or equal, and E is Hausdorff. Let K be a convex subset of E and let C be a nonempty subset of K. Our proofs use a technique based on the investigations of the images of maps and restated for maps f:C×K→R∪{−∞,+∞} of G.X.-Z. Yuan’s results concerning the existence of equilibrium points and minimax inequalities for maps f:K×K→R∪{−∞,+∞}. Examples are provided. 相似文献
5.
Let E be a real Banach space, C be a nonempty closed convex subset of E and T:C→C be a continuous generalized Φ-pseudocontractive mapping. It is proved that T has a unique fixed point in C. 相似文献
6.
If U,V are closed subspaces of a Fréchet space, then E is the direct sum of U and V if and only if E′ is the algebraic direct sum of the annihilators U° and V°. We provide a simple proof of this (possibly well-known) result. 相似文献
7.
Recent optimal scaling theory has produced a condition for the asymptotically optimal acceptance rate of Metropolis algorithms to be the well-known 0.234 when applied to certain multi-dimensional target distributions. These d-dimensional target distributions are formed of independent components, each of which is scaled according to its own function of d. We show that when the condition is not met the limiting process of the algorithm is altered, yielding an asymptotically optimal acceptance rate which might drastically differ from the usual 0.234. Specifically, we prove that as d→∞ the sequence of stochastic processes formed by say the i∗th component of each Markov chain usually converges to a Langevin diffusion process with a new speed measure υ, except in particular cases where it converges to a one-dimensional Metropolis algorithm with acceptance rule α∗. We also discuss the use of inhomogeneous proposals, which might prove to be essential in specific cases. 相似文献
8.
We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces, and we define two classes of monotone mappings between an ordered linear space and a metric space (resp. ordered linear space): K-monotone dominated and cone-to-cone monotone mappings. K-monotone dominated mappings naturally generalize mappings with finite variation (in the classical sense) and K-monotone functions defined by Borwein, Burke and Lewis to mappings with domains and ranges of higher dimensions. First, using results of Veselý and Zají?ek, we show some relationships between these classes. Then, we show that every K-monotone function f:X→R, where X is any Banach space, is continuous outside of a set which can be covered by countably many Lipschitz hypersurfaces. This sharpens a result due to Borwein and Wang. As a consequence, we obtain a similar result for K-monotone dominated and cone-to-cone monotone mappings. Finally, we prove several results concerning almost everywhere differentiability (also in metric and w∗-senses) of these mappings. 相似文献
9.
Let x(s), s∈Rd be a Gaussian self-similar random process of index H. We consider the problem of log-asymptotics for the probability pT that x(s), x(0)=0 does not exceed a fixed level in a star-shaped expanding domain T⋅Δ as T→∞. We solve the problem of the existence of the limit, θ?lim(−logpT)/(logT)D, T→∞, for the fractional Brownian sheet x(s), s∈[0,T]2 when D=2, and we estimate θ for the integrated fractional Brownian motion when D=1. 相似文献
10.
11.
Radu Ioan Boţ Ernö Robert Csetnek Gert Wanka 《Nonlinear Analysis: Theory, Methods & Applications》2007
In this paper we give a weaker sufficient condition for the maximal monotonicity of the operator S+A∗TA, where S:X?X∗, T:Y?Y∗ are two maximal monotone operators, A:X→Y is a linear continuous mapping and X,Y are reflexive Banach spaces. We prove that our condition is weaker than the generalized interior-point conditions given so far in the literature. This condition is formulated using the representative functions of the operators involved. In particular, we rediscover some sufficient conditions given in the past using the so-called Fitzpatrick function for the maximal monotonicity of the sum of two maximal monotone operators and for the precomposition of a maximal monotone operator with a linear operator, respectively. 相似文献
12.
In this paper we establish the boundedness of the extremal solution u∗ in dimension N=4 of the semilinear elliptic equation −Δu=λf(u), in a general smooth bounded domain Ω⊂RN, with Dirichlet data u|∂Ω=0, where f is a C1 positive, nondecreasing and convex function in [0,∞) such that f(s)/s→∞ as s→∞. 相似文献
13.
Consider a face-to-face parallelohedral tiling of Rd and a (d−k)-dimensional face F of the tiling. We prove that the valence of F (i.e. the number of tiles containing F as a face) is not greater than 2k. If the tiling is affinely equivalent to a Voronoi tiling for some lattice (the so called Voronoi case), this gives a well-known upper bound for the number of vertices of a Delaunay k-cell. Yet we emphasize that such an affine equivalence is not assumed in the proof. 相似文献
14.
Michel Mandjes Petteri Mannersalo Ilkka Norros Miranda van Uitert 《Stochastic Processes and their Applications》2006
Consider events of the form {Zs≥ζ(s),s∈S}, where Z is a continuous Gaussian process with stationary increments, ζ is a function that belongs to the reproducing kernel Hilbert space R of process Z, and S⊂R is compact. The main problem considered in this paper is identifying the function β∗∈R satisfying β∗(s)≥ζ(s) on S and having minimal R-norm. The smoothness (mean square differentiability) of Z turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when ζ(s)=s for s∈[0,1] and Z is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process. 相似文献
15.
In this paper, we consider a continuous map f:X→X, where X is a compact metric space, and prove that for any positive integer N, f is Schweizer–Smital chaotic if and only if fN is too. 相似文献
16.
Let H be a real Hilbert space. Let K,F:H→H be bounded, continuous and monotone mappings. Suppose that u∗∈H is a solution to the Hammerstein equation u+KFu=0. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the Hammerstein equation. Furthermore, we give some examples to show that our result is interdisciplinary in nature, covers a large variety of areas and should be of much interest to a wide audience. 相似文献
17.
We prove that θ∗ as previously defined [Int. J. Contemp. Math. Sci. 5 (2010) 721] is the smallest equivalence relation such that the quotient structure R/θ∗ is a commutative fundamental ring. We also investigate some properties with respect to the commutative fundamental relation θ∗ on a hyperring R. 相似文献
18.
This paper investigates the T policy M/G/1 queue with server breakdowns, and startup times. Customers arrive at the system according to a Poisson process. Service times, repair times, and startup times are assumed to be generally distributed. The server is turned on after a fixed length of time T repeatedly until at least one customer is present in the waiting line. The server needs a startup time before starting the service. We analyze various system performance measures and develop the total expected cost function per unit time in which T is a decision variable. We determine the optimum threshold T∗ and derive analytical results for sensitivity investigations. The sensitivity analysis is particularly valuable to the system analyst when evaluating future conditions. We also present extensive numerical computation for illustration purpose. 相似文献
19.
Jean-Stéphane Dhersin Fabian Freund Arno Siri-Jégousse Linglong Yuan 《Stochastic Processes and their Applications》2013
In this paper, we consider Beta(2−α,α) (with 1<α<2) and related Λ-coalescents. If T(n) denotes the length of a randomly chosen external branch of the n-coalescent, we prove the convergence of nα−1T(n) when n tends to ∞, and give the limit. To this aim, we give asymptotics for the number σ(n) of collisions which occur in the n-coalescent until the end of the chosen external branch, and for the block counting process associated with the n-coalescent. 相似文献
20.
We prove that if for a continuous map f on a compact metric space X, the chain recurrent set, R(f) has more than one chain component, then f does not satisfy the asymptotic average shadowing property. We also show that if a continuous map f on a compact metric space X has the asymptotic average shadowing property and if A is an attractor for f, then A is the single attractor for f and we have A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if M is a compact manifold which is not finite with dimM=2, then the C1 interior of the set of all C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of Ω-stable diffeomorphisms. 相似文献