Parallel hybrid methods for generalized equilibrium problems and asymptotically strictly pseudocontractive mappings

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• 作者：Dang Van Hieu
• 关键词：Hybrid method ; Equilibrium problem ; Strictly pseudocontractive mapping ; Parallel computation
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：53
• 期：1-2
• 页码：531-554
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theory of Computation; Mathematics of Computing;
• 出版者：Springer Berlin Heidelberg
• ISSN：1865-2085
• 卷排序：53

文摘

In this paper, we propose two novel parallel hybrid methods for finding a common element of the set of solutions of a finite family of generalized equilibrium problems for monotone bifunctions \(\left\{ f_i\right\} _{i=1}^N\) and \(\alpha \)-inverse strongly monotone operators \(\left\{ A_i\right\} _{i=1}^N\) and the set of common fixed points of a finite family of (asymptotically) \(\kappa \)-strictly pseudocontractive mappings \(\left\{ S_j\right\} _{j=1}^M\) in Hilbert spaces. The strong convergence theorems are established under the standard assumptions imposed on equilibrium bifunctions and operators. Some numerical examples are presented to illustrate the efficiency of the proposed parallel methods.