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Strong convergence of an iterative algorithm for variational inequalities in Banach spaces

✍ Scribed by Yonghong Yao; Stefan Maruster

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
208 KB
Volume
54
Category
Article
ISSN
0895-7177

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Let E be a uniformly convex Banach space having a uniformly GΓ’teaux differentiable norm, D a nonempty closed convex subset of E, and T : D β†’ K (E) a nonself multimap such that F (T ) = βˆ… and P T is nonexpansive, where F (T ) is the fixed point set of T , K (E) is the family of nonempty compact subse

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In this paper, we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self-mappings defined on a nonempty closed convex subset of a reflexive Banach space. We prove that the sequence of approximate solutions generated by the proposed iterative algorithm