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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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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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We first generalize the results of León-Saavedra and Müller (2006) [10] on hypercyclic subspaces to sequences of operators on Fréchet spaces with a continuous norm. Then we study the particular case of iterates of an operator T and show a simple criterion for having no hypercyclic subspace. Finally we deduce from this criterion a characterization of weighted shifts with hypercyclic subspaces on the spaces lp or c0, on the space of entire functions and on certain Köthe sequence spaces. We also prove that if P is a non-constant polynomial and D is the differentiation operator on the space of entire functions then P(D) possesses a hypercyclic subspace. 相似文献
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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
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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
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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
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Under the assumption that E is a reflexive Banach space whose norm is uniformly Gêteaux differentiable and which has a weakly continuous duality mapping Jφ with gauge function φ, Ceng–Cubiotti–Yao [Strong convergence theorems for finitely many nonexpansive mappings and applications, Nonlinear Analysis 67 (2007) 1464–1473] introduced a new iterative scheme for a finite commuting family of nonexpansive mappings, and proved strong convergence theorems about this iteration. In this paper, only under the hypothesis that E is a reflexive Banach space which has a weakly continuous duality mapping Jφ with gauge function φ, and several control conditions about the iterative coefficient are removed, we present a short and simple proof of the above theorem. 相似文献
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In this article we calculate the asymptotic behaviour of the point spectrum for some special self-adjoint unbounded Jacobi operators J acting in the Hilbert space l2=l2(N). For given sequences of positive numbers λn and real qn the Jacobi operator is given by J=SW+WS*+Q, where Q=diag(qn) and W=diag(λn) are diagonal operators, S is the shift operator and the operator J acts on the maximal domain. We consider a few types of the sequences {qn} and {λn} and present three different approaches to the problem of the asymptotics of eigenvalues of various classes of J's. In the first approach to asymptotic behaviour of eigenvalues we use a method called successive diagonalization, the second approach is based on analytical models that can be found for some special J's and the third method is based on an abstract theorem of Rozenbljum. 相似文献
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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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Rolando Cavazos-Cadena Daniel Hernández-Hernández 《Nonlinear Analysis: Theory, Methods & Applications》2012
Given a monotone and homogeneous self-mapping f of the n-dimensional positive cone, a family of contractive mappings is used to define an equivalence relation in the index set, as well as a total order among the equivalence classes. Then, it is shown (i) that the cycle times are well-defined at each index belonging to the maximal and minimal classes, and (ii) that the cycle times of f exist at every index whenever a weak convexity condition is satisfied. 相似文献