Abstract
A hybrid iterative algorithm with Meir-Keeler contraction is presented for solving the fixed point problem of the pseudocontractive mappings and the variational inequalities. Strong convergence analysis is given aslimn→∞d(STxn,TSxn).
Highlights
Throughout, we assume that H is a real Hilbert space with the inner ⟨⋅, ⋅⟩ and the norm ‖ ⋅ ‖ and C ⊂ H is a nonempty closed convex set.Definition 1
One of our purposes of this paper is to find the fixed points of the pseudocontractive mappings in Hilbert spaces
The first interesting algorithm for finding the fixed points of the Lipschitz pseudocontractive mappings in Hilbert spaces was presented by Ishikawa [4] in 1974
Summary
Throughout, we assume that H is a real Hilbert space with the inner ⟨⋅, ⋅⟩ and the norm ‖ ⋅ ‖ and C ⊂ H is a nonempty closed convex set.Definition 1. One of our purposes of this paper is to find the fixed points of the pseudocontractive mappings in Hilbert spaces. The first interesting algorithm for finding the fixed points of the Lipschitz pseudocontractive mappings in Hilbert spaces was presented by Ishikawa [4] in 1974. Ishikawa proved that the sequence {xn} generated by (4) converges strongly to a fixed point of T provided C is a compact set.
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