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Search Results: 1 - 10 of 188 matches for " Fumiaki Kohsaka "
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Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
Fumiaki Kohsaka,Wataru Takahashi
Abstract and Applied Analysis , 2004, DOI: 10.1155/s1085337504309036
Abstract: We first introduce a modified proximal point algorithm formaximal monotone operators in a Banach space. Next, we obtain astrong convergence theorem for resolvents of maximal monotoneoperators in a Banach space which generalizes the previous resultby Kamimura and Takahashi in a Hilbert space. Using this result,we deal with the convex minimization problem and the variationalinequality problem in a Banach space.
Existence of Fixed Points of Firmly Nonexpansive-Like Mappings in Banach Spaces
Koji Aoyama,Fumiaki Kohsaka
Fixed Point Theory and Applications , 2010, DOI: 10.1155/2010/512751
Abstract: The aim of this paper is to obtain some existence theorems related to a hybrid projection method and a hybrid shrinking projection method for firmly nonexpansive-like mappings (mappings of type (P)) in a Banach space. The class of mappings of type (P) contains the classes of resolvents of maximal monotone operators in Banach spaces and firmly nonexpansive mappings in Hilbert spaces.
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
Kohsaka Fumiaki,Takahashi Wataru
Fixed Point Theory and Applications , 2007,
Abstract: Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces.
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
Fumiaki Kohsaka,Wataru Takahashi
Fixed Point Theory and Applications , 2007, DOI: 10.1155/2007/21972
Abstract: Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces.
Existence of Fixed Points of Firmly Nonexpansive-Like Mappings in Banach Spaces
Aoyama Koji,Kohsaka Fumiaki
Fixed Point Theory and Applications , 2010,
Abstract: The aim of this paper is to obtain some existence theorems related to a hybrid projection method and a hybrid shrinking projection method for firmly nonexpansive-like mappings (mappings of type (P)) in a Banach space. The class of mappings of type (P) contains the classes of resolvents of maximal monotone operators in Banach spaces and firmly nonexpansive mappings in Hilbert spaces.
Strong convergence theorems for strongly relatively nonexpansive sequences and applications
Koji Aoyama,Yasunori Kimura,Fumiaki Kohsaka
Mathematics , 2012,
Abstract: The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem for a maximal monotone operator and the fixed point problem for a relatively nonexpansive mapping.
Information-theoretic temporal Bell inequality and quantum computation
Fumiaki Morikoshi
Physics , 2006, DOI: 10.1103/PhysRevA.73.052308
Abstract: An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality is an immediate consequence of the quantumness in the computation. Furthermore, this approach suggests a notion of temporal nonlocality in quantum computation.
Entanglement measure and distance
Fumiaki Morikoshi
Physics , 1999,
Abstract: Recently a new entanglemenet dilution scheme has been constructed by Lo and Popescu. This paper points out that this result has a deep implication that the entanglement measure for bipartite pure states is independent of the distance between entangled two systems.
Recovery of entanglement lost in entanglement manipulation
Fumiaki Morikoshi
Physics , 1999, DOI: 10.1103/PhysRevLett.84.3189
Abstract: When an entangled state is transformed into another one with probability one by local operations and classical communication, the quantity of entanglement decreases. This letter shows that entanglement lost in the manipulation can be partially recovered by an auxiliary entangled pair. As an application, a maximally entangled pair can be obtained from two partially entangled pairs with probability one. Finally, this recovery scheme reveals a fundamental property of entanglement relevant to the existence of incomparable states.
On birational superrigidity and conditional birational superrigidity of certain Fano hypersurfaces
Fumiaki Suzuki
Mathematics , 2015,
Abstract: We prove birational superrigidity of every hypersurface of degree N in P^N with singular locus of dimension s, under the assumption that N is at least 2s+8 and it has only quadratic singularities of rank at least N-s. Combined with the results of I. A. Chel'tsov and T. de Fernex, this completes the list of birationally superrigid singular hypersurfaces with only ordinary double points except in dimension 4 and 6. Further we impose an additional condition on the base locus of a birational map to a Mori fiber space. Then we prove conditional birational superrigidity of certain smooth Fano hypersurfaces of index larger or equal to 2, and birational superrigidity of smooth Fano complete intersections of index 1 in weak form.
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