Fixexd point theory and applications | |
Strong and weak convergence theorems for an infinite family of nonexpansive mappings and applications | |
JC Yao1  LC Ceng2  NC Wong3  | |
[1] Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan;Department of Mathematics, Shanghai Normal University, Shanghai, China;Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China | |
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; | |
DOI : 10.1186/1687-1812-2012-117 | |
学科分类:数学(综合) | |
来源: SpringerOpen | |
【 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. MSC:47H17, 47H09, 47H10, 47H05.
【 授权许可】
CC BY
【 预 览 】
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