Strong and weak convergence theorems for asymptotically nonexpansive mappings
By Charles E. Chidume, Eric Uwadiegwu Ofoedu, Habz Zegeye. 2003
192 citations recorded by the source corpus.
Abstract Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T :K→E be an asymptotically nonexpansive nonself-map with sequence {kn}n⩾1⊂[1,∞), limkn=1, F(T):={x∈K: Tx=x}≠∅ . Suppose {xn}n⩾1 is generated iteratively by x 1 ∈K, x n+1 =P (1−α n )x n +α n T(PT) n−1 x n , n⩾1, where {αn}n⩾1⊂(0,1) is such that ϵ 0. It is proved that (I−T) is demiclosed at 0. Moreover, if ∑n⩾1(kn2−1) x ∗ ∈F(T) is proved. If T is not assumed to be completely continuous but E also has a Frechet differentiable norm, then weak convergence of {xn} to some x ∗ ∈F(T) is obtained.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Immunology
View Paper: https://www.semanticscholar.org/paper/8657421fffac4a0f1c355f4dac5c5e5cdc907fe1
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Citations in the corpus
- Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense (2009, unknown): “[3–5,10,14,17–19,21,23,24,27] and references therein).”
- Weak and strong convergence theorems for finite families of asymptotically nonexpansive mappings in Banach spaces (2007, background): “Our results extend and improve the recently announced ones [4-8,10,15,16,22,24,26,27,30,31] and many others.”
- Approximating fixed points of total asymptotically nonexpansive mappings (2006, background): “More recently, Chidume et al. [14] proved the convergence theorems for asymptotically nonexpansive nonself-mappings in Banach spaces by having extended the corresponding results of [12] [27] [30].”