Abstract
In this article, we introduce a new mapping generated by infinite family of nonexpansive mapping and infinite real numbers. By means of the new mapping, we prove a strong convergence theorem for finding a common element of the set of fixed point problems of infinite family of nonexpansive mappings and the set of a finite family of variational inclusion problems in Hilbert space. In the last section, we apply our main result to prove a strong convergence theorem for finding a common element of the set of fixed point problems of infinite family of strictly pseudo-contractive mappings and the set of finite family of variational inclusion problems.
Highlights
Let H be a real Hilbert space and let C be a nonempty closed convex subset of H
The problem for finding a common fixed point of a family of nonexpansive mappings has been studied by many authors
The well-known convex feasibility problem reduces to finding a point in the intersection of the fixed point sets of a family of nonexpansive mappings
Summary
Let H be a real Hilbert space and let C be a nonempty closed convex subset of H. The problem for finding a common fixed point of a family of nonexpansive mappings has been studied by many authors. The well-known convex feasibility problem reduces to finding a point in the intersection of the fixed point sets of a family of nonexpansive mappings (see, e.g., [2,3]). A mapping A of C into H is called inverse-strongly monotone, see [4], if there exists a positive real number a such that x − y, Ax − Ay ≥ α Ax − Ay 2 for all x, y Î C. Under suitable conditions of {sn}, {rn}{an}, g, they proved that {xn} converges strongly to an element of the set of variational inequality problem and the set of a common fixed point of a finite family of nonexpansive mappings.
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