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- Title
APPROXIMATING FIXED POINTS OF NON-SELF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES.
- Authors
Yongfu Su; Xiaolong Qin
- 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 mapping with {kn} ⊂ [1,∞) such that Σ∞n=1(kn - 1) < ∞ and F(T) is nonempty, where F(T) denotes the fixed points set of T. Let {αn}, {α'n}, and {α''n } be real sequences in (0,1) and ε ≤ αn,α'n,α''n ≤ 1- ε for all n ∈ ℕ and some ε > 0. Starting from arbitrary x1 ∈ K, define the sequence {xn} by x1 ∈ K, zn = P(α''n T(PT)n-1xn +(1- α''n )xn), yn = P(α'nT(PT)n-1zn +(1-α'n)xn), xn+1 = P(αnT(PT)n-1 yn +(1-αn)xn). (i) If the dual E* of E has the Kadec-Klee property, then {xn} converges weakly to a fixed point p ∈ F(T); (ii) if T satisfies condition (A), then {xn} converges strongly to a fixed point p ∈ F(T).
- Subjects
FIXED point theory; ASYMPTOTIC expansions; BANACH spaces; GENERALIZED spaces; MATHEMATICAL mappings; CONTINUOUS functions
- Publication
Journal of Applied Mathematics & Stochastic Analysis, 2006, p1
- ISSN
1048-9533
- Publication type
Article
- DOI
10.1155/JAMSA/2006/21961