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2012 An Iterative Algorithm on Approximating Fixed Points of PseudocontractiveMappings
Youli Yu
J. Appl. Math. 2012(SI03): 1-11 (2012). DOI: 10.1155/2012/341953

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:KK a contractive mapping and T:KK be a uniformly continuous pseudocontractive mapping with F(T). Let {λn}(0,1/2) be a sequence satisfying the following conditions: (i) limnλn=0; (ii) n=0λn=. Define the sequence {xn} in K by x0K, xn+1=λnf(xn)+(12λn)xn+λnTxn, for all n0. Under some appropriate assumptions, we prove that the sequence {xn} converges strongly to a fixed point pF(T) which is the unique solution of the following variational inequality: f(p)p,j(zp)0, for all zF(T).

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Youli Yu. "An Iterative Algorithm on Approximating Fixed Points of PseudocontractiveMappings." J. Appl. Math. 2012 (SI03) 1 - 11, 2012. https://doi.org/10.1155/2012/341953

Information

Published: 2012
First available in Project Euclid: 15 February 2012

zbMATH: 1295.47104
MathSciNet: MR2846451
Digital Object Identifier: 10.1155/2012/341953

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI03 • 2012
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