The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Abdellah Bnouhachem - One of the best experts on this subject based on the ideXlab platform.
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a hybrid iterative method for a combination of equilibria problem a combination of variational inequality problems and a hierarchical fixed point problem
Fixed Point Theory and Applications, 2014Co-Authors: Abdellah BnouhachemAbstract:In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a combination of variational inequality problems, a combination of equilibria problem, and a hierarchical fixed point problem in the setting of Real Hilbert Space. Under appropriate conditions we derive the strong convergence results for this method. Several special cases are also discussed. Preliminary numerical experiments are included to verify the theoretical assertions of the proposed method. The results presented in this paper extend and improve some well-known results in the literature. MSC: 49J30, 47H09, 47J20.
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strong convergence algorithm for split equilibrium problems and hierarchical fixed point problems
The Scientific World Journal, 2014Co-Authors: Abdellah BnouhachemAbstract:The purpose of this paper is to investigate the problem of finding the approximate element of the common set of solutions of a split equilibrium problem and a hierarchical fixed point problem in a Real Hilbert Space. We establish the strong convergence of the proposed method under some mild conditions. Several special cases are also discussed. Our main result extends and improves some well-known results in the literature.
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algorithms of common solutions for a variational inequality a split equilibrium problem and a hierarchical fixed point problem
Fixed Point Theory and Applications, 2013Co-Authors: Abdellah BnouhachemAbstract:In this paper, we suggest and analyze an iterative scheme for finding an approximate element of the common set of solutions of a split equilibrium problem, a variational inequality problem and a hierarchical fixed point problem in a Real Hilbert Space. We also consider the strong convergence of the proposed method under some conditions. Results proved in this paper may be viewed as an improvement and refinement of the previously known results. MSC:49J30, 47H09, 47J20.
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an iterative method for approximating the common solutions of a variational inequality a mixed equilibrium problem and a hierarchical fixed point problem
Journal of Inequalities and Applications, 2013Co-Authors: Abdellah Bnouhachem, Muhammad Aslam NoorAbstract:In this paper, we suggest and analyze an iterative scheme for finding the approximate element of the common set of solutions of a generalized equilibrium problem, a variational inequality problem and a hierarchical fixed point problem in a Real Hilbert Space. We also consider the strong convergence of the proposed method under some conditions. Results proved in this paper may be viewed as an improvement and refinement of the previously known results. MSC: 49J30; 47H09; 47J20
Poom Kumam - One of the best experts on this subject based on the ideXlab platform.
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Two strongly convergent methods governed by pseudo-monotone bi-function in a Real Hilbert Space with applications
Journal of Applied Mathematics and Computing, 2021Co-Authors: Kanikar Muangchoo, Habib Ur Rehman, Poom KumamAbstract:Many iterative schemes have already been developed to solve the equilibrium problems, one of which is the most efficient two-step extragradient method. The objective of this research is to propose two new iterative methods with inertial effect to solve equilibrium problems. These iterative methods are based on an extra-gradient method and a Mann-type iterative method. Two strong convergence theorems have been proved in the setting of Real Hilbert Space, with mild assumptions that the underlying bi-function is Lipschitz-type continuous and pseudo-monotone. The primary advantage of the second method is that it does not require the information of the Lipschitz-type bi-functional constants. We have also studied the applications of our research results to solve particular classes of equilibrium problems. Numerical studies are carried out to show the behaviour of proposed methods and to compare them with the existing ones in the literature.
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viscosity type method for solving pseudomonotone equilibrium problems in a Real Hilbert Space with applications
AIMS Mathematics, 2021Co-Authors: Habib Ur Rehman, Poom Kumam, Kanokwan SitthithakerngkietAbstract:The aim of this article is to introduce a new algorithm by integrating a viscosity-type method with the subgradient extragradient algorithm to solve the equilibrium problems involving pseudomonotone and Lipschitz-type continuous bifunction in a Real Hilbert Space. A strong convergence theorem is proved by the use of certain mild conditions on the bifunction as well as some restrictions on the iterative control parameters. Applications of the main results are also presented to address variational inequalities and fixed-point problems. The computational behaviour of the proposed algorithm on various test problems is described in comparison to other existing algorithms.
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a new popov s subgradient extragradient method for two classes of equilibrium programming in a Real Hilbert Space
Optimization, 2020Co-Authors: Habib Ur Rehman, Poom Kumam, Qiaoli Dong, Yu Peng, Wejdan DeebaniAbstract:In this paper, we proposed two different methods for solving pseudomonotone and strongly pseudomonotone equilibrium problems. We can examine these methods as an extension and improvement of the Pop...
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a weak convergence self adaptive method for solving pseudomonotone equilibrium problems in a Real Hilbert Space
Mathematics, 2020Co-Authors: Pasakorn Yordsorn, Poom Kumam, Habib Ur Rehman, Abdulkarim Hassan IbrahimAbstract:In this paper, we presented a modification of the extragradient method to solve pseudomonotone equilibrium problems involving the Lipschitz-type condition in a Real Hilbert Space. The method uses an inertial effect and a formula for stepsize evaluation, that is updated for each iteration based on some previous iterations. The key advantage of the algorithm is that it is achieved without previous knowledge of the Lipschitz-type constants and also without any line search procedure. A weak convergence theorem for the proposed method is well established by assuming mild cost bifunction conditions. Many numerical experiments are presented to explain the computational performance of the method and to equate them with others.
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the inertial sub gradient extra gradient method for a class of pseudo monotone equilibrium problems
Symmetry, 2020Co-Authors: Habib Ur Rehman, Poom Kumam, Wiyada Kumam, Meshal Shutaywi, Wachirapong JirakitpuwapatAbstract:In this article, we focus on improving the sub-gradient extra-gradient method to find a solution to the problems of pseudo-monotone equilibrium in a Real Hilbert Space. The weak convergence of our method is well-established based on the standard assumptions on a bifunction. We also present the application of our results that enable to solve numerically the pseudo-monotone and monotone variational inequality problems, in addition to the particular presumptions required by the operator. We have used various numerical examples to support our well-proved convergence results, and we can show that the proposed method involves a considerable influence over-running time and the total number of iterations.
Jenchih Yao - One of the best experts on this subject based on the ideXlab platform.
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Strong Convergence Theorems by a Hybrid Extragradient-like Approximation Method for Asymptotically Nonexpansive Mappings in the Intermediate Sense in Hilbert Spaces
2016Co-Authors: Ar Naraghirad, Ngaiching Wong, Jenchih YaoAbstract:Abstract. Let C be a nonempty closed convex subset of a Real Hilbert Space H. Let S: C → C be an asymptotically nonexpansive map in the intermediate sense with the fixed point set F (S). Let A: C → H be a Lipschitz continuous map, and V I(C,A) be the set of solutions u ∈ C of the variational inequality 〈Au, v − u 〉 ≥ 0, ∀v ∈ C. The purpose of this work is to introduce a hybrid extragradient-like approximation method for finding a common element in F (S) and V I(C,A). We establish some strong convergence theorems for sequences produced by our iterative method
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hybrid iterative method for finding common solutions of generalized mixed equilibrium and fixed point problems
Fixed Point Theory and Applications, 2012Co-Authors: Luchuan Ceng, Syming Guu, Jenchih YaoAbstract:Recently, Colao et al. (J Math Anal Appl 344:340-352, 2008) introduced a hybrid viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings in a Real Hilbert Space. In this paper, by combining Colao, Marino and Xu’s hybrid viscosity approximation method and Yamada’s hybrid steepest-descent method, we propose a hybrid iterative method for finding a common element of the set GMEP of solutions of a generalized mixed equilibrium problem and the set N=1 Fix (Si) of fixed points of a finite family of nonexpansive mappings {Si} N=1 in a Real Hilbert Space. We prove the strong convergence of the proposed iterative algorithm to an element of N=1 Fix (Si) ∩ GMEP, which is the unique solution of a variational inequality. AMS subject classifications: 49J40; 47J20; 47H09.
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finding common solutions of a variational inequality a general system of variational inequalities and a fixed point problem via a hybrid extragradient method
Fixed Point Theory and Applications, 2011Co-Authors: Luchuan Ceng, Syming Guu, Jenchih YaoAbstract:We propose a hybrid extragradient method for finding a common element of the solution set of a variational inequality problem, the solution set of a general system of variational inequalities, and the fixed-point set of a strictly pseudocontractive mapping in a Real Hilbert Space. Our hybrid method is based on the well-known extragradient method, viscosity approximation method, and Mann-type iteration method. By constrasting with other methods, our hybrid approach drops the requirement of boundedness for the domain in which various mappings are defined. Furthermore, under mild conditions imposed on the parameters we show that our algorithm generates iterates which converge strongly to a common element of these three problems.
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strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities
Mathematical Methods of Operations Research, 2008Co-Authors: Luchuan Ceng, Changyu Wang, Jenchih YaoAbstract:In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a Real Hilbert Space. First, this system of variational inequalities is proven to be equivalent to a fixed point problem of nonexpansive mapping. Second, by using the demi-closedness principle for nonexpansive mappings, we prove that under quite mild conditions the iterative sequence defined by the relaxed extragradient method converges strongly to a solution of this system of variational inequalities. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems.
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convergence analysis of modified hybrid steepest descent methods with variable parameters for variational inequalities
Journal of Optimization Theory and Applications, 2007Co-Authors: Luchuan Zeng, Ngaiching Wong, Jenchih YaoAbstract:Assume that F is a nonlinear operator on a Real Hilbert Space H which is η-strongly monotone and κ-Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed-point sets of a finite number of nonexpansive mappings on H. We construct an iterative algorithm with variable parameters which generates a sequence {xn} from an arbitrary initial point x0 ∊ H. The sequence {xn} is shown to converge in norm to the unique solution u∗ of the variational inequality \(\langle F(u^{\ast}), v - u^{\ast}\rangle \geq 0, \quad \forall v \in C.\)
Habib Ur Rehman - One of the best experts on this subject based on the ideXlab platform.
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Two strongly convergent methods governed by pseudo-monotone bi-function in a Real Hilbert Space with applications
Journal of Applied Mathematics and Computing, 2021Co-Authors: Kanikar Muangchoo, Habib Ur Rehman, Poom KumamAbstract:Many iterative schemes have already been developed to solve the equilibrium problems, one of which is the most efficient two-step extragradient method. The objective of this research is to propose two new iterative methods with inertial effect to solve equilibrium problems. These iterative methods are based on an extra-gradient method and a Mann-type iterative method. Two strong convergence theorems have been proved in the setting of Real Hilbert Space, with mild assumptions that the underlying bi-function is Lipschitz-type continuous and pseudo-monotone. The primary advantage of the second method is that it does not require the information of the Lipschitz-type bi-functional constants. We have also studied the applications of our research results to solve particular classes of equilibrium problems. Numerical studies are carried out to show the behaviour of proposed methods and to compare them with the existing ones in the literature.
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viscosity type method for solving pseudomonotone equilibrium problems in a Real Hilbert Space with applications
AIMS Mathematics, 2021Co-Authors: Habib Ur Rehman, Poom Kumam, Kanokwan SitthithakerngkietAbstract:The aim of this article is to introduce a new algorithm by integrating a viscosity-type method with the subgradient extragradient algorithm to solve the equilibrium problems involving pseudomonotone and Lipschitz-type continuous bifunction in a Real Hilbert Space. A strong convergence theorem is proved by the use of certain mild conditions on the bifunction as well as some restrictions on the iterative control parameters. Applications of the main results are also presented to address variational inequalities and fixed-point problems. The computational behaviour of the proposed algorithm on various test problems is described in comparison to other existing algorithms.
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an accelerated popov s subgradient extragradient method for strongly pseudomonotone equilibrium problems in a Real Hilbert Space with applications
Communications in Mathematics and Applications, 2020Co-Authors: Nopparat Wairojjana, Habib Ur Rehman, Nuttapol Pakkaranang, Chainarong KhanpanukAbstract:In this paper, we introduce a subgradient extragradient method to find the numerical solution of strongly pseudomonotone equilibrium problems with the Lipschitz-type condition on a bifunction in a Real Hilbert Space. The strong convergence theorem for the proposed method is precisely established on the basis of the standard cost bifunction assumptions. The application of our convergence results is also considered in the context of variational inequalities. For numerical analysis, we consider the well-known Nash-Cournot oligopolistic equilibrium model to support our well-established convergence results.
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a new popov s subgradient extragradient method for two classes of equilibrium programming in a Real Hilbert Space
Optimization, 2020Co-Authors: Habib Ur Rehman, Poom Kumam, Qiaoli Dong, Yu Peng, Wejdan DeebaniAbstract:In this paper, we proposed two different methods for solving pseudomonotone and strongly pseudomonotone equilibrium problems. We can examine these methods as an extension and improvement of the Pop...
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a weak convergence self adaptive method for solving pseudomonotone equilibrium problems in a Real Hilbert Space
Mathematics, 2020Co-Authors: Pasakorn Yordsorn, Poom Kumam, Habib Ur Rehman, Abdulkarim Hassan IbrahimAbstract:In this paper, we presented a modification of the extragradient method to solve pseudomonotone equilibrium problems involving the Lipschitz-type condition in a Real Hilbert Space. The method uses an inertial effect and a formula for stepsize evaluation, that is updated for each iteration based on some previous iterations. The key advantage of the algorithm is that it is achieved without previous knowledge of the Lipschitz-type constants and also without any line search procedure. A weak convergence theorem for the proposed method is well established by assuming mild cost bifunction conditions. Many numerical experiments are presented to explain the computational performance of the method and to equate them with others.
Qiaoli Dong - One of the best experts on this subject based on the ideXlab platform.
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a new popov s subgradient extragradient method for two classes of equilibrium programming in a Real Hilbert Space
Optimization, 2020Co-Authors: Habib Ur Rehman, Poom Kumam, Qiaoli Dong, Yu Peng, Wejdan DeebaniAbstract:In this paper, we proposed two different methods for solving pseudomonotone and strongly pseudomonotone equilibrium problems. We can examine these methods as an extension and improvement of the Pop...
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viscosity iteration methods for a split feasibility problem and a mixed equilibrium problem in a Hilbert Space
Fixed Point Theory and Applications, 2012Co-Authors: Binchao Deng, Tong Chen, Qiaoli DongAbstract:In this paper, we consider and analyze two viscosity iteration algorithms (one implicit and one explicit) for finding a common element of the solution set of a mixed equilibrium problem and the set Γ of a split feasibility problem in a Real Hilbert Space. Furthermore, we derive the strong convergence of a viscosity iteration algorithm to an element of under mild assumptions.
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hybrid iterative scheme by a relaxed extragradient method for equilibrium problems a general system of variational inequalities and fixed point problems of a countable family of nonexpansive mappings
Journal of Applied Mathematics, 2012Co-Authors: Qiaoli Dong, Yanni GuoAbstract:Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a Real Hilbert Space. Furthermore, we prove the strong convergence theorem of the studied iterative method. The results of this paper extend and improve the results of Ceng et al., (2008), W. Kumam and P. Kumam, (2009), Yao et al., (2010) and many others.
