The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
Atid Kangtunyakarn - One of the best experts on this subject based on the ideXlab platform.
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strong Convergence Theorem for the modified generalized equilibrium problem and fixed point problem of strictly pseudo contractive mappings
Fixed Point Theory and Applications, 2014Co-Authors: Sarawut Suwannaut, Atid KangtunyakarnAbstract:The purpose of this paper is to modify the generalized equilibrium problem introduced by Ceng et al. (J. Glob. Optim. 43:487-502, 2012) and to introduce the K-mapping generated by a finite family of strictly pseudo-contractive mappings and finite real numbers modifying the results of Kangtunyakarn and Suantai (Nonlinear Anal. 71:4448-4460, 2009). Then we prove the strong Convergence Theorem for finding a common element of the set of fixed points of a finite family of strictly pseudo-contractive mappings and a finite family of the set of solutions of the modified generalized equilibrium problem. Moreover, using our main result, we obtain the additional results related to the generalized equilibrium problem.
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the combination of the set of solutions of equilibrium problem for Convergence Theorem of the set of fixed points of strictly pseudo contractive mappings and variational inequalities problem
Fixed Point Theory and Applications, 2013Co-Authors: Sarawut Suwannaut, Atid KangtunyakarnAbstract:For the purpose of this article, we introduce a new problem using the concept of equilibrium problem and prove the strong Convergence Theorem for finding a common element of the set of fixed points of an infinite family of κi-strictly pseudo contractive mappings and of a finite family of the set of solutions of equilibrium problem and variational inequalities problem. Furthermore, we utilize our main Theorem for the numerical example.
Sarawut Suwannaut - One of the best experts on this subject based on the ideXlab platform.
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strong Convergence Theorem for the modified generalized equilibrium problem and fixed point problem of strictly pseudo contractive mappings
Fixed Point Theory and Applications, 2014Co-Authors: Sarawut Suwannaut, Atid KangtunyakarnAbstract:The purpose of this paper is to modify the generalized equilibrium problem introduced by Ceng et al. (J. Glob. Optim. 43:487-502, 2012) and to introduce the K-mapping generated by a finite family of strictly pseudo-contractive mappings and finite real numbers modifying the results of Kangtunyakarn and Suantai (Nonlinear Anal. 71:4448-4460, 2009). Then we prove the strong Convergence Theorem for finding a common element of the set of fixed points of a finite family of strictly pseudo-contractive mappings and a finite family of the set of solutions of the modified generalized equilibrium problem. Moreover, using our main result, we obtain the additional results related to the generalized equilibrium problem.
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the combination of the set of solutions of equilibrium problem for Convergence Theorem of the set of fixed points of strictly pseudo contractive mappings and variational inequalities problem
Fixed Point Theory and Applications, 2013Co-Authors: Sarawut Suwannaut, Atid KangtunyakarnAbstract:For the purpose of this article, we introduce a new problem using the concept of equilibrium problem and prove the strong Convergence Theorem for finding a common element of the set of fixed points of an infinite family of κi-strictly pseudo contractive mappings and of a finite family of the set of solutions of equilibrium problem and variational inequalities problem. Furthermore, we utilize our main Theorem for the numerical example.
Wataru Takahashi - One of the best experts on this subject based on the ideXlab platform.
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a strong Convergence Theorem by the shrinking projection method for the split common null point problem in banach spaces
Numerical Functional Analysis and Optimization, 2016Co-Authors: Mayumi Hojo, Wataru TakahashiAbstract:ABSTRACTIn this article, we consider the split common null point problem in Banach spaces. Then, using the shrinking projection method, we prove a strong Convergence Theorem for finding a solution of the split common null point problem in Banach spaces. It appears that such a Theorem is a first in Banach spaces.
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Weak and Strong Convergence Theorems for Positively Homogenuous Nonexpansive Mappings in Banach Spaces
Taiwanese Journal of Mathematics, 2011Co-Authors: Wataru TakahashiAbstract:Our purpose in this paper is first to prove a weak Convergence Theorem by Mann's iteration for positively homogeneous nonexpansive mappings in a Banach space. Further, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove a strong Convergence Theorem for such mappings. From two results, we obtain weak and strong Convergence Theorems for linear contractive mappings in a Banach space. These results are new even if the mappings are linear and contractive.
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Weak and strong Convergence Theorems for nonspreading mappings in Hilbert spaces
Nonlinear Analysis-theory Methods & Applications, 2010Co-Authors: Yu Kurokawa, Wataru TakahashiAbstract:Abstract In this paper, we first obtain a weak mean Convergence Theorem of Baillon’s type for nonspreading mappings in a Hilbert space. Further, using an idea of mean Convergence, we prove a strong Convergence Theorem for nonspreading mappings in a Hilbert space.
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strong Convergence Theorem by a hybrid method for nonexpansive mappings and lipschitz continuous monotone mappings
Siam Journal on Optimization, 2006Co-Authors: N Nadezhkina, Wataru TakahashiAbstract:In this paper we introduce an iterative process for finding a 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 two well-known methods: hybrid and extragradient. We obtain a strong Convergence Theorem for three sequences generated by this process. Based on this result, we also construct an iterative process for finding a common fixed point of two mappings, such that one of these mappings is nonexpansive and the other is taken from the more general class of Lipschitz pseudocontractive mappings.
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weak Convergence Theorem by an extragradient method for nonexpansive mappings and monotone mappings
Journal of Optimization Theory and Applications, 2006Co-Authors: N Nadezhkina, Wataru TakahashiAbstract: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
Wing Shing Wong - One of the best experts on this subject based on the ideXlab platform.
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Convergence Theorem for a general class of power control algorithms
IEEE Transactions on Communications, 2004Co-Authors: Kin K Leung, Chi Wan Sung, Wing Shing WongAbstract:We consider the Convergence issues of distributed power-control algorithms for mobile cellular systems. A Convergence Theorem for power-control algorithms of canonical type is proved. Our result generalizes Yates' framework and provides a new outlook on the problem. The general applicability of the Theorem is demonstrated by showing that many well-known distributed algorithms are canonical. Furthermore, by devising some new discrete algorithms, we exemplify how the Theorem can be used to aid new design.
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Convergence Theorem for a general class of power control algorithms
International Conference on Communications, 2001Co-Authors: Kin K Leung, Chi Wan Sung, Wing Shing WongAbstract:We consider the Convergence issues of distributed power control algorithms for mobile cellular systems. A Convergence Theorem for power control algorithms of canonical type is proven. Our result generalizes Yates' (1995) framework and provides a new outlook on the problem. The general applicability of the Theorem is demonstrated by showing that all the well-known algorithms are canonical. Furthermore, by devising a new discrete algorithm, we exemplify how the Theorem can be used to aid new design.
Yeongcheng Liou - One of the best experts on this subject based on the ideXlab platform.
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Convergence Theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings
Fixed Point Theory and Applications, 2007Co-Authors: Yeongcheng LiouAbstract:We introduce an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of infinite nonexpansive mappings in a Hilbert space. We prove a strong-Convergence Theorem under mild assumptions on parameters.