A hybrid viscosity iterative method with averaged mappings for split equilibrium problems and fixed point problems

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• 作者：P. Majee ; C. Nahak
• 关键词：Nonexpansive mapping ; Averaged mapping ; Split equilibrium problem ; Strong convergence ; Variational inequality problem ; Fixed point problem
• 刊名：Numerical Algorithms
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：74
• 期：2
• 页码：609-635
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Numeric Computing; Algorithms; Algebra; Theory of Computation; Numerical Analysis;
• 出版者：Springer US
• ISSN：1572-9265
• 卷排序：74

文摘

In this paper, with the help of averaged mappings, we introduce and study a hybrid iterative method to approximate a common solution of a split equilibrium problem and a fixed point problem of a finite collection of nonexpansive mappings. We prove that the sequences generated by the iterative scheme strongly converges to a common solution of the above-said problems. We give some numerical examples to ensure that our iterative scheme is more efficient than the methods of Plubtieng and Punpaeng (J. Math Anal. Appl. 336(1), 455–469, 15), Liu (Nonlinear Anal. 71(10), 4852–4861, 10) and Wen and Chen (Fixed Point Theory Appl. 2012(1), 1–15, 18). The results presented in this paper are the extension and improvement of the recent results in the literature.