A viscosity hybrid steepest-descent method for a system of equilibrium and fixed point problems for an infinite family of strictly pseudo-contractive mappings

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作者：
Uamporn Witthayarat
Jong Kyu Kim
Poom Kumam
机构：
[1] King Mongkut’s University of Technology Thonburi,Department of Mathematics, Faculty of Science
[2] KMUTT,Department of Mathematics Education
[3] Kyungnam University,undefined
来源：
Journal of Inequalities and Applications | / 2012卷
关键词：
common fixed point; equilibrium problem; hybrid steepest-descent method; iterative algorithm; nonexpansive mapping; variational inequality;
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摘要：
Based on a viscosity hybrid steepest-descent method, in this paper, we introduce an iterative scheme for finding a common element of a system of equilibrium and fixed point problems of an infinite family of strictly pseudo-contractive mappings which solves the variational inequality 〈(γf−μF)q,p−q〉≤0 for p∈⋂i=1∞F(Ti). Furthermore, we also prove the strong convergence theorems for the proposed iterative scheme and give a numerical example to support and illustrate our main theorem.
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