Abstract
In this paper, we are interested in variational inequalities and fixed-point problems in Hilbert spaces. We present an iterative algorithm for finding a solution of the studied variational inequalities and fixed-point problems. We show the strong convergence of the suggested algorithm.
Highlights
Let H be a real Hilbert space with inner product h·, · i and norm ∥·∥
Where GVIðC, f, φÞ denotes the solution set of the generalized variational inequality which is to find a point x† ∈ C such that
VIðC, gÞ means the solution set of the variational inequality which is to find a point x† ∈ C such that gÀx†
Summary
Let C ⊂ H be a nonempty closed convex set. We will investigate the following variational inequalities and fixed-point problems of finding a point u† such that u† ∈ GVIðC, f , φÞ, φÀu†Á ∈ VIðC, gÞ ∩ FixðTÞ, ð1Þ Where GVIðC, f , φÞ denotes the solution set of the generalized variational inequality (shortly, GVI) which is to find a point x† ∈ C such that Iterative algorithms for solving variational inequalities and fixed-point problems have been investigated extensively by many authors [25–33].
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