Implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and Lipschitz-continuous monotone mappings

Ceng, Lu-Chuan; Sahu, D.R.; Yao, Jen‐Chih

doi:10.1016/j.cam.2009.11.035

Cited by 10 publications

(1 citation statement)

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“…The idea of an extragradient iterative process was first introduced by Korpelevich in [7]. When S : C C is a uniformly continuous asymptotically nonexpansive mapping in the intermediate sense, a hybrid extragradient-like approximation method was proposed by Ceng et al [8,Theorem 1.1] to ensure the weak convergence of some algorithms for finding a member of F(S) ∩ VI(C, A). Meanwhile, assuming S is nonexpansive, Ceng et al in [9] introduced an iterative process and proved its strong convergence to a member of F(S) ∩ VI(C, A).…”

Section: Introductionmentioning

confidence: 99%

Strong convergence theorems by a hybrid extragradient-like approximation method for asymptotically nonexpansive mappings in the intermediate sense in Hilbert spaces

2011

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Let C be a nonempty closed convex subset of a real Hilbert space H. Let S : C C be an asymptotically nonexpansive map in the intermediate sense with the fixed point set F(S). Let A : C H be a Lipschitz continuous map, and VI(C, A) be the set of solutions u C of the variational inequalityThe purpose of this study is to introduce a hybrid extragradient-like approximation method for finding a common element in F(S) and VI(C, A). We establish some strong convergence theorems for sequences produced by our iterative method.

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Section: Introductionmentioning

confidence: 99%