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A variable Krasnosel’skiĭ–Mann algorithm and the multiple-set split feasibility problem. (English) Zbl 1126.47057
This paper is about a variable Krasnosel’skij–Mann algorithm x n+1 =(1-α n )x n +α n T n x n in Banach spaces and its weak convergence to a fixed point of the mapping T. Here, {α n } is a sequence in [0,1] and {T n } is a sequence of nonexpansive mappings such that T n x converges to Tx for every x. Furthermore, the author applies his result to solve the split feasibility problem, i.e., finding a point x such that xC and AxQ, where C and Q are closed convex convex subsets of Hilbert spaces. The algorithm is also generalized for solving multiple-set split feasibility problems. It would have been helpful if some examples had been used to illustrate the process.

47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
65J10Equations with linear operators (numerical methods)
49J53Set-valued and variational analysis