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Search Results: 1 - 10 of 56 matches for " Plubtieng Somyot "
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Iterative Schemes for Fixed Points of Relatively Nonexpansive Mappings and Their Applications
Somyot Plubtieng,Wanna Sriprad
Abstract and Applied Analysis , 2010, DOI: 10.1155/2010/301305
Abstract: We present two iterative schemes with errors which are proved to be strongly convergent to a common element of the set of fixed points of a countable family of relatively nonexpansive mappings and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space. Using the result we consider strong convergence theorems for variational inequalities and equilibrium problems in a real Hilbert space and strong convergence theorems for maximal monotone operators in a real uniformly smooth and uniformly convex Banach space. 1. Introduction Let be a real Banach space, and the dual space of . The function is denoted by for all , where is the normalized duality mapping from to . Let be a closed convex subset of , and let be a mapping from into itself. We denote by the set of fixed points of . A point in is said to be an asymptotic fixed point of [1] if contains a sequence which converges weakly to such that the strong equals 0. The set of asymptotic fixed points of will be denoted by . A mapping from into itself is called nonexpansive if for all and nonexpansive with respect to the Lyapunov functional [2] if for all and it is called relatively nonexpansive [3–6] if and for all and . The asymptotic behavior of relatively nonexpansive mapping was studied in [3–6]. There are many methods for approximating fixed points of a nonexpansive mapping. In 1953, Mann [7] introduced the iteration as follows: a sequence is defined by where the initial guess element is arbitrary and is a real sequence in . Mann iteration has been extensively investigated for nonexpansive mappings. One of the fundamental convergence results was proved by Reich [1]. In an infinite-dimensional Hilbert space, Mann iteration can yield only weak convergence (see [8, 9]). Attempts to modify the Mann iteration method (1.2) so that strong convergence is guaranteed have recently been made. Nakajo and Takahashi [10] proposed the following modification of Mann iteration method (1.2) for nonexpansive mapping in a Hilbert space: in particular, they studied the strong convergence of the sequence generated by where and is the metric projection from onto . Recently, Takahashi et al. [11] extended iteration (1.6) to obtain strong convergence to a common fixed point of a countable family of nonexpansive mappings; let be a nonempty closed convex subset of a Hilbert space . Let and be families of nonexpansive mappings of into itself such that and let . Suppose that satisfies the NST-condition (I) with ; that is, for each bounded
Strong and Weak Convergence of Modified Mann Iteration for New Resolvents of Maximal Monotone Operators in Banach Spaces
Somyot Plubtieng,Wanna Sriprad
Abstract and Applied Analysis , 2009, DOI: 10.1155/2009/795432
Abstract: We prove strong and weak convergence theorems for a new resolvent of maximal monotone operators in a Banach space and give an estimate of the convergence rate of the algorithm. Finally, we apply our convergence theorem to the convex minimization problem. The result present in this paper extendand improve the corresponding result of Ibaraki and Takahashi (2007), and Kim and Xu (2005).
Implicit iteration process of nonexpansive non-self-mappings
Somyot Plubtieng,Rattanaporn Punpaeng
International Journal of Mathematics and Mathematical Sciences , 2005, DOI: 10.1155/ijmms.2005.3103
Abstract: Suppose C is a nonempty closed convex subset of real Hilbert space H. Let T:C→H be a nonexpansive non-self-mapping and P is the nearest point projection of H onto C. In this paper, we study the convergence of the sequences {xn}, {yn}, {zn} satisfying xn=(1−αn)u
Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces
Somyot Plubtieng,Rabian Wangkeeree
International Journal of Mathematics and Mathematical Sciences , 2005, DOI: 10.1155/ijmms.2005.1685
Abstract: Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T:C→C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point of T.
System of Nonlinear Set-Valued Variational Inclusions Involving a Finite Family of -Accretive Operators in Banach Spaces
Prapairat Junlouchai,Somyot Plubtieng
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/560248
Abstract: We study a new system of nonlinear set-valued variational inclusions involving a finite family of (?,?)-accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite family of (?,?)-accretive operators, we prove the existence of the solution for the system of nonlinear set-valued variational inclusions. Moreover, we introduce a new iterative scheme and prove a strong convergence theorem for finding solutions for this system.
Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems
Kamonrat Sombut,Somyot Plubtieng
Abstract and Applied Analysis , 2013, DOI: 10.1155/2013/430409
Abstract:
Existence Solutions of Vector Equilibrium Problems and Fixed Point of Multivalued Mappings
Kanokwan Sitthithakerngkiet,Somyot Plubtieng
Abstract and Applied Analysis , 2013, DOI: 10.1155/2013/952021
Abstract:
Weak Convergence Theorems for a System of Mixed Equilibrium Problems and Nonspreading Mappings in a Hilbert Space
Somyot Plubtieng,Kamonrat Sombut
Journal of Inequalities and Applications , 2010, DOI: 10.1155/2010/246237
Abstract: We introduce an iterative sequence and prove a weak convergence theorem for finding a solution of a system of mixed equilibrium problems and the set of fixed points of a quasi-nonexpansive mapping in Hilbert spaces. Moreover, we apply our result to obtain a weak convergence theorem for finding a solution of a system of mixed equilibrium problems and the set of fixed points of a nonspreading mapping. The result obtained in this paper improves and extends the recent ones announced by Moudafi (2009), Iemoto and Takahashi (2009), and many others. Using this result, we improve and unify several results in fixed point problems and equilibrium problems.
Existence Results for System of Variational Inequality Problems with Semimonotone Operators
Plubtieng Somyot,Sombut Kamonrat
Journal of Inequalities and Applications , 2010,
Abstract: We introduce the system of variational inequality problems for semimonotone operators in reflexive Banach space. Using the Kakutani-Fan-Glicksberg fixed point theorem, we obtain some existence results for system of variational inequality problems for semimonotone with finite-dimensional continuous operators in real reflexive Banach spaces. The results presented in this paper extend and improve the corresponding results for variational inequality problems studied in recent years.
Existence Results for System of Variational Inequality Problems with Semimonotone Operators
Somyot Plubtieng,Kamonrat Sombut
Journal of Inequalities and Applications , 2010, DOI: 10.1155/2010/251510
Abstract:
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