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Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm, let K be a nonempty closed convex subset of E, and let T:K?E be a continuous pseudocontraction which satisfies the weakly inward condition. For f:K?K any contraction map on K, and every nonempty closed convex and bounded subset of K having the fixed point property for nonexpansive self-mappings, it is shown that the path x→xt,t∈[0,1), in K, defined by xt=tTxt+(1−t)f(xt) is continuous and strongly converges to the fixed point of T, which is the unique solution of some co-variational inequality. If, in particular, T is a Lipschitz pseudocontractive self-mapping of K, it is also shown, under appropriate conditions on the sequences of real numbers {αn},{μn}, that the iteration process: z1∈K, zn+1=μn(αnTzn+(1−αn)zn)+(1−μn)f(zn),n∈N, strongly converges to the fixed point of T, which is the unique solution of the same co-variational inequality. Our results propose viscosity approximation methods for Lipschitz pseudocontractions. 相似文献
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Let (Ut,Vt) be a bivariate Lévy process, where Vt is a subordinator and Ut is a Lévy process formed by randomly weighting each jump of Vt by an independent random variable Xt having cdf F. We investigate the asymptotic distribution of the self-normalized Lévy process Ut/Vt at 0 and at ∞. We show that all subsequential limits of this ratio at 0 (∞) are continuous for any nondegenerate F with finite expectation if and only if Vt belongs to the centered Feller class at 0 (∞). We also characterize when Ut/Vt has a non-degenerate limit distribution at 0 and ∞. 相似文献
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Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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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
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Let K be a nonempty closed convex subset of a Banach space E, T:K→K a continuous pseudo-contractive mapping. Suppose that {αn} is a real sequence in [0,1] satisfying appropriate conditions; then for arbitrary x0∈K, the Mann type implicit iteration process {xn} given by xn=αnxn−1+(1−αn)Txn,n≥0, strongly and weakly converges to a fixed point of T, respectively. 相似文献
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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
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We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ?σ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ?. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ?→0 and of (α,β) for Δ→0 and ?→0 without any condition linking ? and Δ. We compare the estimators obtained with various methods and for various magnitudes of Δ and ? based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework. 相似文献
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We consider the Mosco convergence of the sets of fixed points for one-parameter strongly continuous semigroups of nonexpansive mappings. One of our main results is the following: Let C be a closed convex subset of a Hilbert space E. Let {T(t):t≥0} be a strongly continuous semigroup of nonexpansive mappings on C. The set of all fixed points of T(t) is denoted by F(T(t)) for each t≥0. Let τ be a nonnegative real number and let {tn} be a sequence in R satisfying τ+tn≥0 and tn≠0 for n∈N, and limntn=0. Then {F(T(τ+tn))} converges to ?t≥0F(T(t)) in the sense of Mosco. 相似文献
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We consider a multidimensional diffusion X with drift coefficient b(Xt,α) and diffusion coefficient εa(Xt,β) where α and β are two unknown parameters, while ε is known. For a high frequency sample of observations of the diffusion at the time points k/n, k=1,…,n, we propose a class of contrast functions and thus obtain estimators of (α,β). The estimators are shown to be consistent and asymptotically normal when n→∞ and ε→0 in such a way that ε−1n−ρ remains bounded for some ρ>0. The main focus is on the construction of explicit contrast functions, but it is noted that the theory covers quadratic martingale estimating functions as a special case. In a simulation study we consider the finite sample behaviour and the applicability to a financial model of an estimator obtained from a simple explicit contrast function. 相似文献
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In this paper we generalize to unbounded convex subsets C of hyperbolic spaces results obtained by W.A. Kirk and R. Espínola on approximate fixed points of nonexpansive mappings in product spaces (C×M)∞, where M is a metric space and C is a nonempty, convex, closed and bounded subset of a normed or a CAT(0)-space. We extend the results further, to families (Cu)u∈M of unbounded convex subsets of a hyperbolic space. The key ingredient in obtaining these generalizations is a uniform quantitative version of a theorem due to Borwein, Reich and Shafrir, obtained by the authors in a previous paper using techniques from mathematical logic. Inspired by that, we introduce in the last section the notion of uniform approximate fixed point property for sets C and classes of self-mappings of C. The paper ends with an open problem. 相似文献
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We show strong and weak convergence for Mann iteration of multivalued nonexpansive mappings T in a Banach space. Furthermore, we give a strong convergence of the modified Mann iteration which is independent of the convergence of the implicit anchor-like continuous path zt∈tu+(1−t)Tzt. 相似文献
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Let ηt be a Poisson point process of intensity t≥1 on some state space Y and let f be a non-negative symmetric function on Yk for some k≥1. Applying f to all k-tuples of distinct points of ηt generates a point process ξt on the positive real half-axis. The scaling limit of ξt as t tends to infinity is shown to be a Poisson point process with explicitly known intensity measure. From this, a limit theorem for the m-th smallest point of ξt is concluded. This is strengthened by providing a rate of convergence. The technical background includes Wiener–Itô chaos decompositions and the Malliavin calculus of variations on the Poisson space as well as the Chen–Stein method for Poisson approximation. The general result is accompanied by a number of examples from geometric probability and stochastic geometry, such as k-flats, random polytopes, random geometric graphs and random simplices. They are obtained by combining the general limit theorem with tools from convex and integral geometry. 相似文献
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Brooks’ theorem is a fundamental result in the theory of graph coloring. Catlin proved the following strengthening of Brooks’ theorem: Let d be an integer at least 3, and let G be a graph with maximum degree d. If G does not contain Kd+1 as a subgraph, then G has a d-coloring in which one color class has size α(G). Here α(G) denotes the independence number of G. We give a unified proof of Brooks’ theorem and Catlin’s theorem. 相似文献
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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献