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- W2000520329 abstract "Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E∗, and K be a nonempty closed convex subset of E. Suppose that {Tn}(n=1,2,…) is a uniformly asymptotically regular sequence of nonexpansive mappings from K into itself such that F≔⋂n=1∞F(Tn)≠0̸. For arbitrary initial value x0∈K and fixed contractive mapping f:K→K, define iteratively a sequence {xn} as follows: xn+1=λn+1f(xn)+(1−λn+1)Tn+1xn,n≥0, where {λn}⊂(0,1) satisfies limn→∞λn=0 and ∑n=1∞λn=∞. We prove that {xn} converges strongly to p∈F, as n→∞, where p is the unique solution in F to the following variational inequality: 〈(I−f)p,j(p−u)〉≤0for all u∈F(T). Our results extend and improve the corresponding ones given by O’Hara et al. [J.G. O’Hara, P. Pillay, H.-K. Xu, Iterative approaches to finding nearest common fixed point of nonexpansive mappings in Hilbert spaces, Nonlinear Anal. 54 (2003) 1417–1426], J.S. Jung [Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 302 (2005) 509–520], H.K. Xu [Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004) 279–291] and O’Hara et al. [J.G. O’Hara, P. Pillay, H.-K. Xu, Iterative approaches to convex feasibility problem in Banach space, Nonlinear Anal. Available online 20 October 2005. doi:10.1016/j.na.2005.07.36]." @default.
- W2000520329 created "2016-06-24" @default.
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- W2000520329 date "2007-02-01" @default.
- W2000520329 modified "2023-09-28" @default.
- W2000520329 title "Iterative approximation to common fixed points of nonexpansive mapping sequences in reflexive Banach spaces" @default.
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- W2000520329 doi "https://doi.org/10.1016/j.na.2005.12.004" @default.
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