Abstract
In this paper, we investigate the problem of finding some common element in the set of common fixed points of an infinite family of nonexpansive mappings and in the set of solutions of variational inequalities based on an extragradient-like iterative algorithm. Strong convergence of the purposed iterative algorithm is obtained.
Highlights
Iterative algorithms have been playing an important role in the approximation solvability, especially of nonlinear variational inequalities as well as of nonlinear equations in several fields such as mechanics, traffic, economics, information, medicine, and many others
The well-known convex feasibility problem which captures applications in various disciplines such as image restoration and radiation therapy treatment planning is to find a point in the intersection of common fixed point sets of a family of nonlinear mappings; see, for example, [ – ]
It is known that Mann iterative algorithm only has weak convergence for nonexpansive mappings in infinite-dimensional Hilbert spaces; see [ ] for more details and the references therein
Summary
Iterative algorithms have been playing an important role in the approximation solvability, especially of nonlinear variational inequalities as well as of nonlinear equations in several fields such as mechanics, traffic, economics, information, medicine, and many others. It is known that Mann iterative algorithm only has weak convergence for nonexpansive mappings in infinite-dimensional Hilbert spaces; see [ ] for more details and the references therein.
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