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An implicit iterative scheme for an infinite countable family of asymptotically nonexpansive mappings in Banach spaces. (English) Zbl 1172.47058
The authors consider a nonempty closed convex subset K of a reflexive Banach space E with a weakly continuous dual mapping, and {T i } i=1 , an infinite family of asymptotically nonexpansive mappings with the sequence {k in } satisfying k in 1 for each i=1,2, n=1,2,, and lim n k in =1 for each i=1,2,. They introduce a new implicit iterative scheme generated by {T i } i=1 and prove that the scheme converges strongly to a common fixed point of {T i } i=1 , which solves a certain variational inequality.
MSC:
47J25Iterative procedures (nonlinear operator equations)
49J40Variational methods including variational inequalities
47H05Monotone operators (with respect to duality) and generalizations
47H09Mappings defined by “shrinking” properties
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47J20Inequalities involving nonlinear operators
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