Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012, Special Issue (2012), Article ID 341953, 11 pages.
An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings
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 a contractive mapping and be a uniformly continuous pseudocontractive mapping with . Let be a sequence satisfying the following conditions: (i) ; (ii) . Define the sequence in K by , , for all . Under some appropriate assumptions, we prove that the sequence converges strongly to a fixed point which is the unique solution of the following variational inequality: , for all .
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 341953, 11 pages.
First available in Project Euclid: 15 February 2012
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Yu, Youli. An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings. J. Appl. Math. 2012, Special Issue (2012), Article ID 341953, 11 pages. doi:10.1155/2012/341953. https://projecteuclid.org/euclid.jam/1329337705