Abstract
Recently, Yao et al. (2011) introduced two algorithms for solving a system of nonlinear variational inequalities. In this paper, we consider two general algorithms and obtain the extension results for computing fixed points of nonexpansive mappings in Banach spaces. Moreover, the fixed points solve the same system of nonlinear variational inequalities.
Highlights
Let X be a real Banach space and let C be a nonempty closed convex subset of X
Recall that a mapping T : C → C is said to be nonexpansive if T x − T y ≤ x − y, for all x, y ∈ C
They proved that the above algorithms converge strongly to some solutions of a system of nonlinear inequalities, which involves finding x∗, y∗ ∈ C × C
Summary
Let X be a real Banach space and let C be a nonempty closed convex subset of X. Let q be a given real number with 1 < q ≤ 2 and let X be a q-uniformly smooth Banach space. Let C be a nonempty bounded closed convex subset of a uniformly convex Banach space X and let T be a nonexpansive mapping of C into itself. Let {xn} and {zn} be bounded sequences in Banach space E and {γn} be a sequence in 0, 1 which satisfies the following condition:
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