Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications

被引：0
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作者：
LC Ceng
NC Wong
JC Yao
机构：
[1] Shanghai Normal University,Department of Mathematics
[2] Scientific Computing Key Laboratory of Shanghai Universities,Department of Applied Mathematics
[3] National Sun Yat-sen University,Center for General Education
[4] Kaohsiung Medical University,undefined
来源：
Fixed Point Theory and Applications | / 2012卷
关键词：
hybrid viscosity approximation method; nonexpansive mapping; strictly convex Banach space; uniformly smooth Banach space; reflexive Banach space with weakly continuous duality map;
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摘要：
In this paper, let E be a reflexive and strictly convex Banach space which either is uniformly smooth or has a weakly continuous duality map. We consider the hybrid viscosity approximation method for finding a common fixed point of an infinite family of nonexpansive mappings in E. We prove the strong convergence of this method to a common fixed point of the infinite family of nonexpansive mappings, which solves a variational inequality on their common fixed point set. We also give a weak convergence theorem for the hybrid viscosity approximation method involving an infinite family of nonexpansive mappings in a Hilbert space.
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