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1.
Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings   总被引:18,自引:0,他引:18  
In this paper, we introduce an iteration process of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for an inverse strongly-monotone mapping, and then obtain a weak convergence theorem. Using this result, we obtain a weak convergence theorem for a pair of a nonexpansive mapping and a strictly pseudocontractive mapping. Further, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping.  相似文献
2.
In this paper, we study the convergence of the sequence defined by

where and is a nonexpansive mapping from a closed convex subset of a Banach space into itself.

  相似文献

3.
The local index formula in noncommutative geometry   总被引:13,自引:0,他引:13  
In noncommutative geometry a geometric space is described from a spectral vantage point, as a tripleA, H, D consisting of a *-algebraA represented in a Hilbert spaceH together with an unbounded selfadjoint operatorD, with compact resolvent, which interacts with the algebra in a bounded fashion. This paper contributes to the advancement of this point of view in two significant ways: (1) by showing that any pseudogroup of transformations of a manifold gives rise to such a spectral triple of finite summability degree, and (2) by proving a general, in some sense universal, local index formula for arbitrary spectral triples of finite summability degree, in terms of the Dixmier trace and its residue-type extension.We dedicate this paper to Misha Gromov  相似文献
4.
Chaotic Attractors with Discrete Planar Symmetries   总被引:11,自引:0,他引:11  
Chaotic behavior is known to be compatible with symmetry and illustrations are constructed using functions equivariant with respect to the desired symmetries. Earlier investigations determined families of equivariant functions for a few of the discrete symmetry groups in the plane; those results are extended to all the discrete symmetry groups of the plane. This includes consideration of the all the frieze and two-dimensional crystallographic groups. © 1998 Elsevier Science Ltd. All rights reserved.  相似文献
5.
A note on the three color problem   总被引:11,自引:0,他引:11  
It is shown that a planar graph withouti-circuits, 4 i 9, is 3-colorable. This result strengthens the result obtained by H.L. Abbott and B. Zhou.The author's research was partially supported by the Office of Naval Research, Grant number N00014-92-J-1965.  相似文献
6.
In this paper, we prove a strong convergence theorem for relatively nonexpansive mappings in a Banach space by using the hybrid method in mathematical programming. Using this result, we also discuss the problem of strong convergence concerning nonexpansive mappings in a Hilbert space and maximal monotone operators in a Banach space.  相似文献
7.
Curve shortening makes convex curves circular   总被引:10,自引:0,他引:10  
8.
In this paper, we introduce an iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The iterative process is based on the so-called extragradient method. We obtain a weak convergence theorem for two sequences generated by this process  相似文献
9.
Transportation cost for Gaussian and other product measures   总被引:9,自引:0,他引:9  
Consider the canonical Gaussian measure N on , a probability measure on N , absolutely continuous with respect to N . We prove that the transportation cost of to N , when the cost of transporting a unit of mass fromx toy is measured by xy2, is at most d. As a consequence we obtain a completely elementary proof of a very sharp form of the concentration of measure phenomenon in Gauss space. We then prove a result of the same nature when N is replaced by the measure of density 2N exp (– iN |x i |). This yields a sharp form of concentration of measure in that space.Work partially supported by an NSF Grant.  相似文献
10.
Martingale transforms and Hardy spaces   总被引:9,自引:0,他引:9  
Summary Burkholder's martingale transforms are especially useful in studying predictable martingale Hardy spaces. Characterizations of such spaces via martingale transforms are provided. In particular, it is shown that for 0<p<, a martingale inh p , defined by the conditioned square function, is the martingale transform of a bmo2 martingale with a multiplier sequence whose maximal function is inL p .  相似文献
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