Firstly, the concept of projective nonexpansive mappings is presented in this paper. The approximate solvability of a generalized system for relaxedcocoercive and involving projective nonexpansive mapping nonlinear v...
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(纸本)9783037853078
Firstly, the concept of projective nonexpansive mappings is presented in this paper. The approximate solvability of a generalized system for relaxedcocoercive and involving projective nonexpansive mapping nonlinear variational inequalities in Hilbert spaces is studied, based on the convergence of projection methods. The results presented in this paper extend and improve the main results of many authors.
In this paper, we introduce and study a new hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive ma...
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In this paper, we introduce and study a new hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for a xi-Lipschitz continuous and relaxed (m, v)-cocoercivemappings in Hilbert spaces. Then, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm which solves some optimization problems under some suitable conditions. Our results extend and improve the recent results of Yao et al. [V. Yao, M.A. Noor, S. Zainab and Y.C. Liou, Mixed equilibrium problems and optimization problems, J. Math. Anal. Appl (2009). doi:10.1016/***.2008.12.005] and Gao and Guo [X. Gao and Y. Guo, Strong convergence theorem of a modified iterative algorithm for Mixed equilibrium problems in Hilbert spaces, J. Inequal. Appl. (2008). doi:10.1155/2008/454181] and many others. (C) 2009 Elsevier Ltd. All rights reserved.
In this article, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of common fixed points of a finite family of non-expansive mappings and the set of solutions of a ...
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In this article, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of common fixed points of a finite family of non-expansive mappings and the set of solutions of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Our results improve and extend the recent ones announced by Iiduka and Tahakshi [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005), pp. 341-350] and many others.
A new system for relaxedcocoercive non-linear variational inequalities in uniformly smooth Banach spaces is introduced and studied using the convergence of projection *** results generalize and improve the correspond...
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A new system for relaxedcocoercive non-linear variational inequalities in uniformly smooth Banach spaces is introduced and studied using the convergence of projection *** results generalize and improve the corresponding results of recent works.
The approximate solvability of a generalized system for relaxedcocoercive nonlinear variational inequality in Hilbert spaces is studied, based on the convergence of projection methods. The results presented in this p...
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The approximate solvability of a generalized system for relaxedcocoercive nonlinear variational inequality in Hilbert spaces is studied, based on the convergence of projection methods. The results presented in this paper extend and improve the main results of [R.U. Verma, Generalized system for relaxedcocoercive variational inequalities and its projection methods, J. Optim. Theory Appl. 121 (1) (2004) 203-210;R.U. Verma, Generalized class of partial relaxed monotonicity and its connections, Adv. Nonlinear Var. Inequal. 7 (2) (2004) 155-164;R.U. Verma, General convergence analysis for two-step projection methods and applications to variational problems, Appl. Math. Lett. 18 (11) (2005) 1286-1292;N.H. Xiu, J.Z. Zhang, Local convergence analysis of projection type algorithms: Unified approach, J. Optim. Theory Appl. 115 (2002) 211-230;H. Nie, Z. Liu, K.H. Kim, S.M. Kang, A system of nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings, Adv. Nonlinear Var. Inequal. 6 (2) (2003) 91-99]. (c) 2006 Elsevier Ltd. All rights reserved.
In this article, we introduce and consider a general system of variational inequalities. Using the projection technique, we suggest and analyse new iterative methods for this system of variational inequalities. We als...
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In this article, we introduce and consider a general system of variational inequalities. Using the projection technique, we suggest and analyse new iterative methods for this system of variational inequalities. We also study the convergence analysis of the new iterative method under certain mild conditions. Since this new system includes the system of variational inequalities involving the single operator, variational inequalities and related optimization problems as special cases, results obtained in this article continue to hold for these problems. Our results improve and extend the recent ones announced by many others.
The approximate solvability of a generalized system for relaxedcocoercive mixed variational inequality is studied by using the resolvent operator technique. The results presented in this paper are more general and in...
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The approximate solvability of a generalized system for relaxedcocoercive mixed variational inequality is studied by using the resolvent operator technique. The results presented in this paper are more general and include many previously known results as special cases. (C) 2009 Elsevier Inc. All rights reserved.
The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of ...
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The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxedcocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.
In this paper, we introduce a new and interesting system of generalized mixed quasi-variational-like inclusions with (A, eta, m)-accretive operators and relaxed cocoercive mappings which contains variational inequalit...
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In this paper, we introduce a new and interesting system of generalized mixed quasi-variational-like inclusions with (A, eta, m)-accretive operators and relaxed cocoercive mappings which contains variational inequalities, variational inclusions, systems of variational inequalities, systems of variational-like inequalities and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (A, eta, m)-accretive operators, we prove the existence of solutions and the convergence of a new p-step iterative algorithm for this system of generalized mixed quasi-variational-like inclusions in real q-uniformly smooth Banach spaces. The results in this paper unifies, extends and improves some known results in the literature. (C) 2009 Elsevier B.V. All rights reserved.
In this paper, we introduce a new system of generalized mixed quasi-variational-like inclusions with (A, eta, m)-accretive operators and relaxed cocoercive mappings. By using the fixed point theorem of Nadler, we prov...
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In this paper, we introduce a new system of generalized mixed quasi-variational-like inclusions with (A, eta, m)-accretive operators and relaxed cocoercive mappings. By using the fixed point theorem of Nadler, we prove the existence of solutions for this general system of generalized mixed quasi-variational-like inclusions and its special cases. The results in this paper unify, extend and improve some known results in the literature. The novel proof method is simpler than those iterative algorithm approach for proving the existence of solutions of all classes of system of set-valued variational inclusions in the literature.
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