The Experts below are selected from a list of 5481 Experts worldwide ranked by ideXlab platform
Suthep Suantai - One of the best experts on this subject based on the ideXlab platform.
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Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs
Mathematics, 2019Co-Authors: Suthep Suantai, Mana Donganont, Watcharaporn CholamjiakAbstract:In this paper, we introduce the iterative scheme for finding a common fixed point of a Countable Family of G-nonexpansive mappings by the shrinking projection method which generalizes Takahashi Takeuchi and Kubota’s theorem in a Hilbert space with a directed graph. Simultaneously, we give examples and numerical results for supporting our main theorems and compare the rate of convergence of some examples under the same conditions.
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A new one-step iterative process for approximating common fixed points of a Countable Family of quasi-nonexpansive multi-valued mappings in CAT(0) spaces
Bulletin of The Iranian Mathematical Society, 2017Co-Authors: Suthep Suantai, Bancha Panyanak, Withun PhuengrattanaAbstract:In this paper, we propose a new one-step iterative process for a Countable Family of quasi-nonexpansive multi-valued mappings in a CAT(0) space. We also prove strong and $Delta$-convergence theorems of the proposed iterative process under some control conditions. Our main results extend and generalize many results in the literature.
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Hybrid methods for a mixed equilibrium problem and fixed points of a Countable Family of multivalued nonexpansive mappings
Fixed Point Theory and Applications, 2013Co-Authors: Aunyarat Bunyawat, Suthep SuantaiAbstract:In this paper, we prove a strong convergence theorem for a new hybrid method, using shrinking projection method introduced by Takahashi and a fixed point method for finding a common element of the set of solutions of mixed equilibrium problem and the set of common fixed points of a Countable Family of multivalued nonexpansive mappings in Hilbert spaces. We also apply our main result to the convex minimization problem and the fixed point problem of a Countable Family of multivalued nonexpansive mappings.
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a hybrid method for a Countable Family of lipschitz generalized asymptotically quasi nonexpansive mappings and an equilibrium problem
Communications of The Korean Mathematical Society, 2013Co-Authors: Prasit Cholamjiak, Watcharaporn Cholamjiak, Suthep SuantaiAbstract:In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a Countable Family of uni- formly Lipschitzian generalized asymptotically quasi-nonexpansive map- pings and the solutions set of equilibrium problems. Some strong con- vergence theorems of the proposed iterative scheme are established by using the concept of W-mappings of a Countable Family of uniformly Lip- schitzian generalized asymptotically quasi-nonexpansive mappings.
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Weak and strong convergence theorems for a Countable Family of strict pseudocontractions in Banach spaces
Optimization, 2013Co-Authors: Prasit Cholamjiak, Suthep SuantaiAbstract:We first investigate the weak convergence of the Mann-type iterative scheme for a Countable Family of strict pseudocontractions in a uniformly smooth Banach space which is uniformly convex or satisfies Opial's condition. Then the strong convergence theorems of the modified Mann-type iterative scheme are also proved in a uniformly smooth Banach space. As a consequence, several weak and strong convergence theorems for an infinite Family of pseudocontractions are established.
Poom Kumam - One of the best experts on this subject based on the ideXlab platform.
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Proximal Point Algorithm for a Common of Countable Families of Inverse Strongly Accretive Operators and Nonexpansive Mappings with Convergence Analysis
Mathematical Modelling and Analysis, 2016Co-Authors: Khanittha Promluang, Kanokwan Sitthithakerngkiet, Poom KumamAbstract:In this paper, we investigate and analyze a proximal point algorithm via viscosity approximation method with error. This algorithm is introduced for finding a common zero point for a Countable Family of inverse strongly accretive operators and a Countable Family of nonexpansive mappings in Banach spaces. Our result can be extended to some well known results from a Hilbert space to a uniformly convex and 2−uniformly smooth Banach space. Finally, we establish the strong convergence theorems for the proximal point algorithm. Also, some illustrative numerical examples are presented.
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a hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems
Applied Mathematics and Computation, 2015Co-Authors: Kanokwan Sitthithakerngkiet, Jitsupa Deepho, Poom KumamAbstract:Abstract In this paper, we introduce and study a new viscosity approximation method by modify the hybrid steepest descent method for finding a common solution of split variational inclusion problem and fixed point problem of a Countable Family of nonexpansive mappings. Under suitable conditions, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of the split variational inclusion problem and fixed point problem for a Countable Family of nonexpansive mappings which is the unique solution of the variational inequality problem. The results present in this paper are the supplement, extension and generalization of the previously known results in this area. Numerical results demonstrate the performance and convergence of our result that the algorithm converges to a solution to a concrete split variational inclusion problem and fixed point problem.
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viscosity approximation methods based on generalized contraction mappings for a Countable Family of strict pseudo contractions a general system of variational inequalities and a generalized mixed equilibrium problem in banach spaces
Mathematical and Computer Modelling, 2013Co-Authors: Pongsakorn Sunthrayuth, Poom KumamAbstract:Abstract In this paper, we introduce viscosity approximation methods based on generalized contraction mappings for finding a set of common fixed points of a Countable Family of strict pseudo-contraction mappings, the common element of the set solutions of a general system of variational inequalities with Lipschitzian and relaxed cocoercive mappings and the set of solutions of a generalized mixed equilibrium problem. Furthermore, strong convergence theorems of the purposed iterative process are established in the framework of Banach spaces. The results presented in this paper improve and extend many recent important results.
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Computational of generalized projection method for maximal monotone operators and a Countable Family of relatively quasi-nonexpansive mappings
Optimization, 2013Co-Authors: Siwaporn Saewan, Poom KumamAbstract:AbstractWe introduce a new hybrid projection method in mathematical programming for finding a common element of the set of common fixed points of a Countable Family of relatively quasi-nonexpansive mappings, the set of the variational inequality for an -inverse-strongly monotone operator, the set of solutions of the mixed equilibrium problem and a zero of a maximal monotone operator in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Furthermore, we give some numerical examples which support our main theorem in the last part.
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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.
Qingqing Cheng - One of the best experts on this subject based on the ideXlab platform.
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the approximation of common element for maximal monotone operator generalized mixed equilibrium problem and fixed point problem
Journal of the Egyptian Mathematical Society, 2015Co-Authors: Jingling Zhang, Qingqing ChengAbstract:Abstract The purpose of this paper is to get strong convergence theorems for a Countable Family of relatively quasi-nonexpansive mappings { S n } n = 0 ∞ , a maximal monotone operator T, and a generalized mixed equilibrium problem in a uniformly smooth and uniformly convex Banach space lacking condition UARC. Two examples are given to support our results. One is a Countable Family of uniformly closed relatively quasi-nonexpansive mappings but not a Countable Family of relatively nonexpansive mappings. Another is uniformly closed but not satisfies condition UARC. Many recent results in this field have been unified and improved.
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uniformly closed replaced aktt or aktt condition to get strong convergence theorems for a Countable Family of relatively quasi nonexpansive mappings and systems of equilibrium problems
Fixed Point Theory and Applications, 2014Co-Authors: Jingling Zhang, Qingqing ChengAbstract:The purpose of this paper is to construct a new iterative scheme and to get a strong convergence theorem for a Countable Family of relatively quasi-nonexpansive mappings and a system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space using the properties of generalized f-projection operator. The notion of uniformly closed mappings is presented and an example will be given which is a Countable Family of uniformly closed relatively quasi-nonexpansive mappings but not a Countable Family of relatively nonexpansive mappings. Another example shall be given which is uniformly closed but does not satisfy condition AKTT and ∗AKTT. Our results can be applied to solve a convex minimization problem. In addition, this paper clarifies an ambiguity in a useful lemma. The results of this paper modify and improve many other important recent results.
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Uniformly closed replaced AKTT or ∗ AKTT condition to get strong convergence theorems for a Countable Family of relatively quasi-nonexpansive mappings and systems of equilibrium problems
Fixed Point Theory and Applications, 2014Co-Authors: Jingling Zhang, Qingqing ChengAbstract:The purpose of this paper is to construct a new iterative scheme and to get a strong convergence theorem for a Countable Family of relatively quasi-nonexpansive mappings and a system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space using the properties of generalized f-projection operator. The notion of uniformly closed mappings is presented and an example will be given which is a Countable Family of uniformly closed relatively quasi-nonexpansive mappings but not a Countable Family of relatively nonexpansive mappings. Another example shall be given which is uniformly closed but does not satisfy condition AKTT and ∗AKTT. Our results can be applied to solve a convex minimization problem. In addition, this paper clarifies an ambiguity in a useful lemma. The results of this paper modify and improve many other important recent results.
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convergence theorems of a three step iteration method for a Countable Family of pseudocontractive mappings
Fixed Point Theory and Applications, 2013Co-Authors: Qingqing Cheng, Jingling ZhangAbstract:The purpose of this paper is to construct a three-step iteration method (as follows) and obtain the convergence theorem for a Countable Family of Lipschitz pseudocontractive mappings in Hilbert space H. For the iteration format,
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simple projection algorithm for a Countable Family of weak relatively nonexpansive mappings and applications
Fixed Point Theory and Applications, 2012Co-Authors: Jingling Zhang, Qingqing ChengAbstract:Let E be a uniformly convex and uniformly smooth Banach space, let C be a nonempty closed convex subset of E ,l et{Tn} : C → C be a Countable Family of weak relatively nonexpansive mappings such that F = � ∞=1 F(Tn) � ∅. For any given gauss
Jingling Zhang - One of the best experts on this subject based on the ideXlab platform.
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the approximation of common element for maximal monotone operator generalized mixed equilibrium problem and fixed point problem
Journal of the Egyptian Mathematical Society, 2015Co-Authors: Jingling Zhang, Qingqing ChengAbstract:Abstract The purpose of this paper is to get strong convergence theorems for a Countable Family of relatively quasi-nonexpansive mappings { S n } n = 0 ∞ , a maximal monotone operator T, and a generalized mixed equilibrium problem in a uniformly smooth and uniformly convex Banach space lacking condition UARC. Two examples are given to support our results. One is a Countable Family of uniformly closed relatively quasi-nonexpansive mappings but not a Countable Family of relatively nonexpansive mappings. Another is uniformly closed but not satisfies condition UARC. Many recent results in this field have been unified and improved.
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uniformly closed replaced aktt or aktt condition to get strong convergence theorems for a Countable Family of relatively quasi nonexpansive mappings and systems of equilibrium problems
Fixed Point Theory and Applications, 2014Co-Authors: Jingling Zhang, Qingqing ChengAbstract:The purpose of this paper is to construct a new iterative scheme and to get a strong convergence theorem for a Countable Family of relatively quasi-nonexpansive mappings and a system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space using the properties of generalized f-projection operator. The notion of uniformly closed mappings is presented and an example will be given which is a Countable Family of uniformly closed relatively quasi-nonexpansive mappings but not a Countable Family of relatively nonexpansive mappings. Another example shall be given which is uniformly closed but does not satisfy condition AKTT and ∗AKTT. Our results can be applied to solve a convex minimization problem. In addition, this paper clarifies an ambiguity in a useful lemma. The results of this paper modify and improve many other important recent results.
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Uniformly closed replaced AKTT or ∗ AKTT condition to get strong convergence theorems for a Countable Family of relatively quasi-nonexpansive mappings and systems of equilibrium problems
Fixed Point Theory and Applications, 2014Co-Authors: Jingling Zhang, Qingqing ChengAbstract:The purpose of this paper is to construct a new iterative scheme and to get a strong convergence theorem for a Countable Family of relatively quasi-nonexpansive mappings and a system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space using the properties of generalized f-projection operator. The notion of uniformly closed mappings is presented and an example will be given which is a Countable Family of uniformly closed relatively quasi-nonexpansive mappings but not a Countable Family of relatively nonexpansive mappings. Another example shall be given which is uniformly closed but does not satisfy condition AKTT and ∗AKTT. Our results can be applied to solve a convex minimization problem. In addition, this paper clarifies an ambiguity in a useful lemma. The results of this paper modify and improve many other important recent results.
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convergence theorems of a three step iteration method for a Countable Family of pseudocontractive mappings
Fixed Point Theory and Applications, 2013Co-Authors: Qingqing Cheng, Jingling ZhangAbstract:The purpose of this paper is to construct a three-step iteration method (as follows) and obtain the convergence theorem for a Countable Family of Lipschitz pseudocontractive mappings in Hilbert space H. For the iteration format,
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simple projection algorithm for a Countable Family of weak relatively nonexpansive mappings and applications
Fixed Point Theory and Applications, 2012Co-Authors: Jingling Zhang, Qingqing ChengAbstract:Let E be a uniformly convex and uniformly smooth Banach space, let C be a nonempty closed convex subset of E ,l et{Tn} : C → C be a Countable Family of weak relatively nonexpansive mappings such that F = � ∞=1 F(Tn) � ∅. For any given gauss
Rabian Wangkeeree - One of the best experts on this subject based on the ideXlab platform.
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Iterative approximation methods for mixed equilibrium problems for a Countable Family of quasi-ϕ-asymptotically nonexpansive multivalued mappings in Banach spaces
Fixed Point Theory and Applications, 2013Co-Authors: Rabian Wangkeeree, Pakkapon PreechasilpAbstract:In this paper, we prove the existence of a solution of the mixed equilibrium problem MEP ( f , φ , C ) by using the KKM mapping in a Banach space setting. Then, by virtue of this result, we introduce a hybrid iterative scheme for finding a common element of the set of solutions of MEP ( f , φ , C ) and the set of common fixed points of a Countable Family of quasi-ϕ-asymptotically nonexpansive multivalued mappings. Furthermore, we prove that the sequences generated by the hybrid iterative scheme converge strongly to a common element of the set of solutions of MEP ( f , φ , C ) and the set of common fixed points of a Countable Family of quasi-ϕ-asymptotically nonexpansive multivalued mappings.
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existence and iterative approximation for generalized equilibrium problems for a Countable Family of nonexpansive mappings in banach spaces
Fixed Point Theory and Applications, 2011Co-Authors: Uthai Kamraksa, Rabian WangkeereeAbstract:We first prove the existence of a solution of the generalized equilibrium problem (GEP) using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solution set of a GEP and the fixed point set of Countable Family of nonexpansive mappings in the frameworks of Banach spaces. By means of a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solution set of GEP and common fixed point set of nonexpansive mappings.
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Existence and iterative approximation for generalized equilibrium problems for a Countable Family of nonexpansive mappings in banach spaces
Fixed Point Theory and Applications, 2011Co-Authors: Uthai Kamraksa, Rabian WangkeereeAbstract:We first prove the existence of a solution of the generalized equilibrium problem (GEP) using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solution set of a GEP and the fixed point set of Countable Family of nonexpansive mappings in the frameworks of Banach spaces. By means of a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solution set of GEP and common fixed point set of nonexpansive mappings. AMS Subject Classification: 47H09, 47H10
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Existence theorems and iterative approximation methods for generalized mixed equilibrium problems for a Countable Family of nonexpansive mappings
Journal of Global Optimization, 2011Co-Authors: Uthai Kamraksa, Rabian WangkeereeAbstract:In this paper, we introduce the new generalized mixed equilibrium problem basing on hemicontinuous and relaxed monotonic mapping. Using the KKM technique, we obtain the existence of solutions for the generalized mixed equilibrium problem in a Banach space. Furthermore, we also introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of a Countable Family of nonexpansive mappings. The strong convergence theorem of the proposed sequence is obtained in a Banach space setting. The main results extend various results existing in the current literature.
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New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces
Fixed Point Theory and Applications, 2011Co-Authors: Kamonrat Nammanee, Rabian WangkeereeAbstract:We introduce new general iterative approximation methods for finding a common fixed point of a Countable Family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexive Banach spaces which admit a weakly continuous duality mapping. Finally, we apply our results to solve the the equilibrium problems and the problem of finding a zero of an accretive operator. The results presented in this paper mainly improve on the corresponding results reported by many others.
