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Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces. (English) Zbl 0888.47034

Summary: We study the convergence of the sequence defined by

x 0 C,x n+1 =α n x+(1-α n )Tx n ,n=0,1,2,...,

where 0α n 1 and T is a nonexpansive mapping from a closed convex subset of a Banach space into itself.


MSC:
47H09Mappings defined by “shrinking” properties
47J25Iterative procedures (nonlinear operator equations)
49M05Numerical methods in calculus of variations based on necessary conditions