An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings

Youli Yu

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

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 {λn}⊂(0, 1/2) be a sequence satisfying the following conditions: (i) limn→∞λn = 0; (ii) ∑n=0∞λn=∞. Define the sequence {xn} in K by x0 ∈ K, xn+1 = λnf(xn)+(1 − 2λn)xn + λnTxn, for all n ≥ 0. Under some appropriate assumptions, we prove that the sequence {xn} 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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https://doi.org/10.1155/2012/341953

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:341953

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