Abstract
This article aims to deal with a new modified iterative projection method for solving a hierarchical fixed point problem. It is shown that under certain approximate assumptions of the operators and parameters, the modified iterative sequence { x n } converges strongly to a fixed point x ∗ of T, also the solution of a variational inequality. As a special case, this projection method solves some quadratic minimization problem. The results here improve and extend some recent corresponding results by other authors.MSC:47H10, 47J20, 47H09, 47H05.
Highlights
Let be a nonempty closed convex subset of a real Hilbert space H with the inner product ·, · and the norm ·
A mapping F : −→ H is called η-strongly monotone if there exists a constant η ≥ such that x – y, Fx – Fy ≥ η x – y, ∀x, y ∈
It is well known that the iterative methods for finding hierarchical fixed points of nonexpansive mappings can be used to solve a convex minimization problem; see, for example, [, ] and the references therein
Summary
Let be a nonempty closed convex subset of a real Hilbert space H with the inner product ·, · and the norm ·. Which is equivalent to the following fixed point problem: to find an x∗ ∈ that satisfies x∗ = PFix(T)Sx∗.
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