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Iterative algorithm of solutions for a system of generalized mixed implicity equilibrium problems in reflexive Banach spaces

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APPLIED MATHEMATICS AND COMPUTATION 2012年第9期218卷 4953-4961页

作者： Ding, Xie Ping Sichuan Normal Univ Coll Math & Software Sci Chengdu 610066 Sichuan Peoples R China

In this paper, a new system of generalized mixed implicity equilibrium problems involving non-monotone set-valued mappings is introduced and studied in real reflexive Banach spaces. Following the idea of Moudafi, we consider a system of generalized equations problems and show its equivalence with the system of generalized mixed implicity equilibrium problems. By using a fixed point formulation of the system of generalized equation problems, a new iterative algorithm for solving the system of generalized mixed implicity equilibrium problems is suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new and unify and generalize some recent results in this field. (C) 2011 Elsevier Inc. All rights reserved.

关键词： system of generalized mixed implicity equilibrium problems system of generalized equation problems Iterative algorithm Reflexive Banach spaces

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NEW ITERATIVE ALGORITHM FOR SOLVING A system OF generalized mixed IMPLICIT equilibrium problems IN BANACH SPACES

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TAIWANESE JOURNAL OF MATHEMATICS 2011年第2期15卷 673-695页

作者： Ding, Xie-Ping Ho, Juei-Ling Tainan Univ Technol Dept Finance Tainan 704 Taiwan Sichuan Normal Univ Coll Math & Software Sci Chengdu 610068 Sichuan Peoples R China

A new system of generalized mixed implicity equilibrium problems is introduced and studied in real Banach spaces. The notion of the Yosida approximation introduced by Moudafi in Hilbert spaces is first generalized to reflexive Banach spaces. By using the notion of the Yosida approximation, a system of generalized equation problems is considered and its equivalence with the system of generalized mixed implicity equilibrium problems is also proved. By using the system of generalized equation problems, a new iterative algorithm for solving the system of generalized mixed implicity equilibrium problems is suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new and unify and generalize some recent results in this field.

关键词： system of generalized mixed implicity equilibrium problems Yosida approximation system of generalized equation problems Iterative algorithm Banach spaces

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