Journal of inequalities and applications | |
Three-step Mann iterations for a general system of variational inequalities and an infinite family of nonexpansive mappings in Banach spaces | |
Lu-Chuan Ceng1  | |
关键词: three-step Mann iterations; general system of variational inequalities; infinitely many nonexpansive mappings; sunny nonexpansive retraction; fixed point; strictly convex Banach space; uniformly smooth Banach space; reflexive Banach space with weakly continuous duality map; | |
DOI : 10.1186/1029-242X-2013-539 | |
学科分类:数学(综合) | |
来源: SpringerOpen | |
【 摘 要 】
In this paper, let X be a uniformly convex Banach space which either is uniformly smooth or has a weakly continuous duality map. We introduce and consider three-step Mann iterations for finding a common solution of a general system of variational inequalities (GSVI) and a fixed point problem (FPP) of an infinite family of nonexpansive mappings in X. Here three-step Mann iterations are based on Korpelevich’s extragradient method, the viscosity approximation method and the Mann iteration method. We prove the strong convergence of this method to a common solution of the GSVI and the FPP, which solves a variational inequality on their common solution set. We also give a weak convergence theorem for three-step Mann iterations involving the GSVI and the FPP in a Hilbert space. The results presented in this paper improve, extend, supplement and develop the corresponding results announced in the earlier and very recent literature. MSC:49J30, 47H09, 47J20.
【 授权许可】
CC BY
【 预 览 】
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