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- W2067357943 abstract "Let X be a real strictly convex and reflexive Banach space with a uniformly Gâteaux differentiable norm and C be a nonempty closed convex subset of X. Let {Tn}n=1∞ be a sequence of nonexpansive self-mappings on C such that the common fixed point set F≔⋂n=1∞F(Tn)≠0̸ and f:C→C be a given contractive mapping, and {λn} be a sequence of nonnegative numbers in [0,1]. Consider the following relaxed viscosity approximation method {xn+1=(1−αn−βn)xn+αnf(yn)+βnWnyn,yn=(1−γn)xn+γnWnxn,n≥1 where Wn is the W-mapping generated by Tn,Tn−1,…,T1 and λn,λn−1,…,λ1 for each n≥1. It is proven that under very mild conditions on the parameters, the sequence {xn} of approximate solutions generated by the proposed method converges strongly to some p∈F where p is the unique solution in F to the following variational inequality: 〈(I−f)p,J(p−x∗)〉≤0,∀x∗∈F." @default.
- W2067357943 created "2016-06-24" @default.
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- W2067357943 date "2008-11-01" @default.
- W2067357943 modified "2023-09-28" @default.
- W2067357943 title "Relaxed viscosity approximation methods for fixed point problems and variational inequality problems" @default.
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- W2067357943 doi "https://doi.org/10.1016/j.na.2007.09.019" @default.
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