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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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Given an arbitrarily weak notion of left-〈f〉-porosity and an arbitrarily strong notion of right-〈g〉-porosity, we construct an example of closed subset of R which is not σ -left-〈f〉-porous and is right-〈g〉-porous. We also briefly summarize the relations between three different definitions of porosity controlled by a function; we then observe that our construction gives the example for any combination of these definitions of left-porosity and right-porosity. 相似文献
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Sergey A. Antonyan Natalia Jonard-Pérez Saúl Juárez-Ordóñez 《Journal of Mathematical Analysis and Applications》2014
A compact convex subset K of a topological linear space is called a Keller compactum if it is affinely homeomorphic to an infinite-dimensional compact convex subset of the Hilbert space ?2. Let G be a compact topological group acting affinely on a Keller compactum K and let 2K denote the hyperspace of all non-empty compact subsets of K endowed with the Hausdorff metric topology and the induced action of G . Further, let cc(K) denote the subspace of 2K consisting of all compact convex subsets of K. In a particular case, the main result of the paper asserts that if K is centrally symmetric, then the orbit spaces 2K/G and cc(K)/G are homeomorphic to the Hilbert cube. 相似文献
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This paper is devoted to a problem of finding the smallest positive integer s(m,n,k) such that (m+1) generic skew-symmetric (k+1)-forms in (n+1) variables as linear combinations of the same s(m,n,k) decomposable skew-symmetric (k+1)-forms. 相似文献
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Let F be an algebraically closed field. Let V be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form B over F. Suppose the characteristic of F is sufficiently large , i.e. either zero or greater than the dimension of V. Let I(V,B) denote the group of isometries. Using the Jacobson–Morozov lemma we give a new and simple proof of the fact that two elements in I(V,B) are conjugate if and only if they have the same elementary divisors. 相似文献
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Xiao-Ming Niu Tetsuya Sakurai Hiroshi Sugiura 《Journal of Computational and Applied Mathematics》2007
In this paper, we propose a verified method for bounding clusters of zeros of analytic functions. Our method gives a disk that contains a cluster of m zeros of an analytic function f(z). Complex circular arithmetic is used to perform a validated computation of n -degree Taylor polynomial p(z) of f(z). Some well known formulae for bounding zeros of a polynomial are used to compute a disk containing a cluster of zeros of p(z). A validated computation of an upper bound for Taylor remainder series of f(z) and a lower bound of p(z) on a circle are performed. Based on these results, Rouché's theorem is used to verify that the disk contains the cluster of zeros of f(z). This method is efficient in computation of the initial disk of a method for finding validated polynomial factor of an analytic function. Numerical examples are presented to illustrate the efficiency of the proposed method. 相似文献
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Francesco Altomare Mirella Cappelletti Montano Vita Leonessa Ioan Raşa 《Journal of Mathematical Analysis and Applications》2014
The paper is concerned with a special class of positive linear operators acting on the space C(K) of all continuous functions defined on a convex compact subset K of Rd, d?1, having non-empty interior. Actually, this class consists of all positive linear operators T on C(K) which leave invariant the polynomials of degree at most 1 and which, in addition, map polynomials into polynomials of the same degree. Among other things, we discuss the existence of such operators in the special case where K is strictly convex by also characterizing them within the class of positive projections. In particular we show that such operators exist if and only if ∂K is an ellipsoid. Furthermore, a characterization of balls of Rd in terms of a special class of them is furnished. Additional results and illustrative examples are presented as well. 相似文献
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In this paper we study properties of essential entropy-carrying sets of a continuous map on a compact metric space. If f:X→X is continuous on a compact metric space X, then the intersection of all essential entropy-carrying sets of f may or may not be an essential entropy-carrying set of f . When this intersection is an essential entropy-carrying set we denote it by E(f), the least essential entropy-carrying set, otherwise we say that E(f) does not exist. We present an example where E(f) does not exist but also find a sufficient condition for E(f) to exist. If f is a piecewise monotone map, we show that E(f) exists and is the finite union of the entropy-carrying sets in the Nitecki Decomposition of the nonwandering set of f intersected with the closure of the periodic points of f . When E(f) exists we study how it relates to other entropy-carrying sets of f including subsets of itself. 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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For any n-by-n matrix A , we consider the maximum number k=k(A) for which there is a k-by-k compression of A with all its diagonal entries in the boundary ∂W(A) of the numerical range W(A) of A. If A is a normal or a quadratic matrix, then the exact value of k(A) can be computed. For a matrix A of the form B⊕C, we show that k(A)=2 if and only if the numerical range of one summand, say, B is contained in the interior of the numerical range of the other summand C and k(C)=2. For an irreducible matrix A , we can determine exactly when the value of k(A) equals the size of A . These are then applied to determine k(A) for a reducible matrix A of size 4 in terms of the shape of W(A). 相似文献
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Let G denote a locally compact Hausdorff group and M(G) be the space of all bounded complex-valued regular Borel measures on G . In this paper, we define two strict topologies on M(G) and study various properties of these topologies such as metrizability, barrelledness and completeness. We also determine the dual space of M(G) and consider various continuity properties for the convolution product on M(G) under these topologies. 相似文献
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Let F be an infinite field with characteristic not equal to two. For a graph G=(V,E) with V={1,…,n}, let S(G;F) be the set of all symmetric n×n matrices A=[ai,j] over F with ai,j≠0, i≠j if and only if ij∈E. We show that if G is the complement of a partial k -tree and m?k+2, then for all nonsingular symmetric m×m matrices K over F, there exists an m×n matrix U such that UTKU∈S(G;F). As a corollary we obtain that, if k+2?m?n and G is the complement of a partial k-tree, then for any two nonnegative integers p and q with p+q=m, there exists a matrix in S(G;R) with p positive and q negative eigenvalues. 相似文献