共查询到20条相似文献,搜索用时 421 毫秒
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In this paper, we introduce the metric dG on a G -metric space (X,G) and use this notion to show that many contraction conditions for maps on the G -metric space (X,G) reduce to certain contraction conditions for maps on the metric space (X,dG). As applications, the proofs of many fixed point theorems for maps on the G -metric space (X,G) may be simplified, and many fixed point theorems for maps on the G -metric space (X,G) are direct consequences of preceding results for maps on the metric space (X,dG). 相似文献
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Jean-Pierre Kahane 《Comptes Rendus Mathematique》2014,352(5):383-385
For almost all x>1, (xn)(n=1,2,…) is equidistributed modulo 1, a classical result. What can be said on the exceptional set? It has Hausdorff dimension one. Much more: given an (bn) in [0,1[ and ε>0, the x -set such that |xn−bn|<ε modulo 1 for n large enough has dimension 1. However, its intersection with an interval [1,X] has a dimension <1, depending on ε and X. Some results are given and a question is proposed. 相似文献
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Let (W,S) be a Coxeter system with a strictly complete Coxeter graph. The present paper concerns the set Red(z) of all reduced expressions for any z∈W. By associating each bc-expression to a certain symbol, we describe the set Red(z) and compute its cardinal |Red(z)| in terms of symbols. An explicit formula for |Red(z)| is deduced, where the Fibonacci numbers play a crucial role. 相似文献
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Guang-Xin Huang Feng Yin Ke Guo 《Journal of Computational and Applied Mathematics》2008,217(1):259-267
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This paper treats some variational principles for solutions of inhomogeneous p -Laplacian boundary value problems on exterior regions U?RN with dimension N?3. Existence-uniqueness results when p∈(1,N) are provided in a space E1,p(U) of functions that contains W1,p(U). Functions in E1,p(U) are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an Lp-imbedding theorem. Also an existence result for a general variational problem of this type is obtained. 相似文献
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For any finite-dimensional Hopf algebra H we construct a group homomorphism BiGal(H)→BrPic(Rep(H)), from the group of equivalence classes of H -biGalois objects to the group of equivalence classes of invertible exact Rep(H)-bimodule categories. We discuss the injectivity of this map. We exemplify in the case H=Tq is a Taft Hopf algebra and for this we classify all exact indecomposable Rep(Tq)-bimodule categories. 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
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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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Mohamed Ali Toumi 《Expositiones Mathematicae》2010,28(3):269-275
Let A be an Archimedean f -algebra and let N(A) be the set of all nilpotent elements of A. Colville et al. [4] proved that a positive linear map d:A→A is a derivation if and only if d(A)⊂N(A) and d(A2)={0}, where A2 is the set of all products ab in A. 相似文献
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The determination of an approximate greatest common divisor (GCD) of two inexact polynomials f=f(y) and g=g(y) arises in several applications, including signal processing and control. This approximate GCD can be obtained by computing a structured low rank approximation S*(f,g) of the Sylvester resultant matrix S(f,g). In this paper, the method of structured total least norm (STLN) is used to compute a low rank approximation of S(f,g), and it is shown that important issues that have a considerable effect on the approximate GCD have not been considered. For example, the established works only yield one matrix S*(f,g), and therefore one approximate GCD, but it is shown in this paper that a family of structured low rank approximations can be computed, each member of which yields a different approximate GCD. Examples that illustrate the importance of these and other issues are presented. 相似文献
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