The Experts below are selected from a list of 23016 Experts worldwide ranked by ideXlab platform
Wataru Takahashi - One of the best experts on this subject based on the ideXlab platform.
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approximation of common fixed points of a countable family of nonexpansive mappings in a banach space
Nonlinear Analysis-theory Methods & Applications, 2007Co-Authors: Koji Aoyama, Yasunori Kimura, Wataru Takahashi, Masashi ToyodaAbstract:In this paper, to find a common fixed point of a family of nonexpansive mappings, we introduce a Halpern type Iterative Sequence. Then we prove that such a Sequence converges strongly to a common fixed point of nonexpansive mappings. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings and the problem of finding a zero of an accretive operator.
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block Iterative methods for a finite family of relatively nonexpansive mappings in banach spaces
Fixed Point Theory and Applications, 2007Co-Authors: Fumiaki Kohsaka, Wataru TakahashiAbstract: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.
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weak convergence of an Iterative Sequence for accretive operators in banach spaces
Fixed Point Theory and Applications, 2006Co-Authors: Koji Aoyama, Hideaki Iiduka, Wataru TakahashiAbstract:Let be a nonempty closed convex subset of a smooth Banach space and let be an accretive operator of into . We first introduce the problem of finding a point such that where is the duality mapping of . Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol'shteĭn and Tret'yakov in the Euclidean space to a Banach space. And using our theorem, we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space and so on.
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weak convergence of an Iterative Sequence for accretive operators in banach spaces
Fixed Point Theory and Applications, 2006Co-Authors: Koji Aoyama, Hideaki Iiduka, Wataru TakahashiAbstract:Let be a nonempty closed convex subset of a smooth Banach space and let be an accretive operator of into . We first introduce the problem of finding a point such that where is the duality mapping of . Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol'shteĭn and Tret'yakov in the Euclidean space to a Banach space. And using our theorem, we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space and so on.
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weak and strong convergence theorems for maximal monotone operators in a banach space
Set-valued Analysis, 2004Co-Authors: Shoji Kamimura, Fumiaki Kohsaka, Wataru TakahashiAbstract:In this paper, we introduce an Iterative Sequence for finding a solution of a maximal monotone operator in a uniformly convex Banach space. Then we first prove a strong convergence theorem, using the notion of generalized projection. Assuming that the duality mapping is weakly sequentially continuous, we next prove a weak convergence theorem, which extends the previous results of Rockafellar [SIAM J. Control Optim.14 (1976), 877–898] and Kamimura and Takahashi [J. Approx. Theory106 (2000), 226–240]. Finally, we apply our convergence theorem to the convex minimization problem and the variational inequality problem.
Yeol Je Cho - One of the best experts on this subject based on the ideXlab platform.
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multi step inertial krasnosel skiǐ mann iteration with new inertial parameters arrays
Journal of Fixed Point Theory and Applications, 2021Co-Authors: Qiaoli Dong, Yeol Je Cho, Themistocles M RassiasAbstract:Recently, the authors (Dong et al. in J Global Optim 73(4):801–824, 2019) introduced the multi-step inertial Krasnosel’skiǐ–Mann iteration, where the inertial parameters involve the Iterative Sequence. Therefore, one has to compute the inertial parameters per iteration. The aim of this article is to present two kinds of inertial parameter arrays which do not depend on the Iterative Sequence. We first introduce a general Krasnosel’skiǐ–Mann iteration on the affine hull of orbits, based on which one inertial parameter array is presented. Second, we investigate the other inertial parameter array by introducing a modified Krasnosel’skii-Mann iteration. The convergence of the modified Krasnosel’skiǐ–Mann iteration is shown using an exhaustive convergence analysis and the running-average iteration-complexity bound is provided. Finally, we give two numerical examples to illustrate that the multi-step inertial Krasnosel’skiǐ–Mann iteration with inertial parameters proposed in this article behaves better than that with inertial parameters given in [10].
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the modified mann type Iterative algorithm for a countable family of totally quasi ϕ asymptotically nonexpansive mappings by the hybrid generalized f projection method
Fixed Point Theory and Applications, 2013Co-Authors: Siwaporn Saewan, Poom Kumam, Preedaporn Kanjanasamranwong, Yeol Je ChoAbstract:The purpose of this article is to introduce the modified Mann type Iterative Sequence, using a new technique, by the hybrid generalized f-projection operator for a countable family of totally quasi-ϕ-asymptotically nonexpansive mappings in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Then we prove that the modified Mann type Iterative scheme converges strongly to a common element of the sets of fixed points of the given mappings. Our result extends and improves the results of Li et al. (Comput. Math. Appl. 60:1322-1331, 2010), Takahashi et al. (J. Math. Anal. Appl. 341:276-286, 2008) and many other authors.
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strong convergence theorems of reich type Iterative Sequence for non self asymptotically nonexpansive mappings
Taiwanese Journal of Mathematics, 2007Co-Authors: Shihsen Chang, Yeol Je Cho, Y X TianAbstract:The purpose of this paper is to give some necessary and sufficient conditions for the Iterative Sequence of Reich type to converging to a fixed point. The results presented in this paper extend and improve some recent results ([2-4]).
Johannes Soding - One of the best experts on this subject based on the ideXlab platform.
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hhblits lightning fast Iterative protein Sequence searching by hmm hmm alignment
Nature Methods, 2012Co-Authors: Michael Remmert, Andreas Biegert, Andreas Hauser, Johannes SodingAbstract:Sequence-based protein function and structure prediction depends crucially on Sequence-search sensitivity and accuracy of the resulting Sequence alignments. We present an open-source, general-purpose tool that represents both query and database Sequences by profile hidden Markov models (HMMs): 'HMM-HMM-based lightning-fast Iterative Sequence search' (HHblits; http://toolkit.genzentrum.lmu.de/hhblits/). Compared to the Sequence-search tool PSI-BLAST, HHblits is faster owing to its discretized-profile prefilter, has 50-100% higher sensitivity and generates more accurate alignments.
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hhblits lightning fast Iterative protein Sequence searching by hmm hmm alignment
Nature Methods, 2012Co-Authors: Michael Remme, Andreas Iege, Andreas Hause, Johannes SodingAbstract:HHblits is a protein Sequence search tool that works by Iterative pairwise comparison of profile hidden Markov models. It outperforms existing tools in terms of speed, sensitivity and alignment quality. Sequence-based protein function and structure prediction depends crucially on Sequence-search sensitivity and accuracy of the resulting Sequence alignments. We present an open-source, general-purpose tool that represents both query and database Sequences by profile hidden Markov models (HMMs): 'HMM-HMM–based lightning-fast Iterative Sequence search' (HHblits; http://toolkit.genzentrum.lmu.de/hhblits/ ). Compared to the Sequence-search tool PSI-BLAST, HHblits is faster owing to its discretized-profile prefilter, has 50–100% higher sensitivity and generates more accurate alignments.
Poom Kumam - One of the best experts on this subject based on the ideXlab platform.
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inertial extra gradient method for solving a family of strongly pseudomonotone equilibrium problems in real hilbert spaces with application in variational inequality problem
Symmetry, 2020Co-Authors: Habib Ur Rehman, Poom Kumam, Ioannis K Argyros, Wejdan Deebani, Wiyada KumamAbstract:In this paper, we propose a new method, which is set up by incorporating an inertial step with the extragradient method for solving a strongly pseudomonotone equilibrium problems. This method had to comply with a strongly pseudomonotone property and a certain Lipschitz-type condition of a bifunction. A strong convergence result is provided under some mild conditions, and an Iterative Sequence is accomplished without previous knowledge of the Lipschitz-type constants of a cost bifunction. A sufficient explanation is that the method operates with a slow-moving stepsize Sequence that converges to zero and non-summable. For numerical explanations, we analyze a well-known equilibrium model to support our well-established convergence result, and we can see that the proposed method seems to have a significant consistent improvement over the performance of the existing methods.
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the modified mann type Iterative algorithm for a countable family of totally quasi ϕ asymptotically nonexpansive mappings by the hybrid generalized f projection method
Fixed Point Theory and Applications, 2013Co-Authors: Siwaporn Saewan, Poom Kumam, Preedaporn Kanjanasamranwong, Yeol Je ChoAbstract:The purpose of this article is to introduce the modified Mann type Iterative Sequence, using a new technique, by the hybrid generalized f-projection operator for a countable family of totally quasi-ϕ-asymptotically nonexpansive mappings in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Then we prove that the modified Mann type Iterative scheme converges strongly to a common element of the sets of fixed points of the given mappings. Our result extends and improves the results of Li et al. (Comput. Math. Appl. 60:1322-1331, 2010), Takahashi et al. (J. Math. Anal. Appl. 341:276-286, 2008) and many other authors.
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a hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping
Nonlinear Analysis: Hybrid Systems, 2008Co-Authors: Poom KumamAbstract:The purpose of this paper is to present an Iterative scheme by a hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in the framework of a Hilbert space. We show that the Iterative Sequence converges strongly to a common element of the above three sets under appropriate conditions. Additionally, the idea of our results are applied to find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space.
Fumiaki Kohsaka - One of the best experts on this subject based on the ideXlab platform.
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an implicitly defined Iterative Sequence for monotone operators in banach spaces
Journal of Inequalities and Applications, 2014Co-Authors: Fumiaki KohsakaAbstract:Given a monotone operator in a Banach space, we show that an Iterative Sequence, which is implicitly defined by a fixed point theorem for mappings of firmly nonexpansive type, converges strongly to a minimum norm zero point of the given operator. Applications to a convex minimization problem and a variational inequality problem are also included.
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block Iterative methods for a finite family of relatively nonexpansive mappings in banach spaces
Fixed Point Theory and Applications, 2007Co-Authors: Fumiaki Kohsaka, Wataru TakahashiAbstract: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.
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weak and strong convergence theorems for maximal monotone operators in a banach space
Set-valued Analysis, 2004Co-Authors: Shoji Kamimura, Fumiaki Kohsaka, Wataru TakahashiAbstract:In this paper, we introduce an Iterative Sequence for finding a solution of a maximal monotone operator in a uniformly convex Banach space. Then we first prove a strong convergence theorem, using the notion of generalized projection. Assuming that the duality mapping is weakly sequentially continuous, we next prove a weak convergence theorem, which extends the previous results of Rockafellar [SIAM J. Control Optim.14 (1976), 877–898] and Kamimura and Takahashi [J. Approx. Theory106 (2000), 226–240]. Finally, we apply our convergence theorem to the convex minimization problem and the variational inequality problem.
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strong convergence of an Iterative Sequence for maximal monotone operators in a banach space
Abstract and Applied Analysis, 2004Co-Authors: Fumiaki KohsakaAbstract:We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.
