An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings

Youli Yu

Journal of Applied Mathematics, 2012, vol. 2012, 1-11

Abstract:

Let E be a real reflexive Banach space with a uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed convex subset of E, and every nonempty closed convex bounded subset of K has the fixed point property for non-expansive self-mappings. Let f : K → K a contractive mapping and T : K → K be a uniformly continuous pseudocontractive mapping with F ( T ) ≠∅ . Let { λ n } ⊂ ( 0 , 1 / 2 ) be a sequence satisfying the following conditions: (i) lim n → ∞ λ n = 0 ; (ii) ∑ n = 0 ∞ λ n = ∞ . Define the sequence { x n } in K by x 0 ∈ K , x n + 1 = λ n f ( x n ) + ( 1 − 2 λ n ) x n + λ n T x n , for all n ≥ 0 . Under some appropriate assumptions, we prove that the sequence { x n } converges strongly to a fixed point p ∈ F ( T ) which is the unique solution of the following variational inequality: 〈 f ( p ) − p , j ( z − p ) 〉 ≤ 0 , for all z ∈ F ( T ) .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:341953

DOI: 10.1155/2012/341953

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