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

Youli Yu

Full-text: Open access

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 ) .

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 341953, 11 pages.

Dates
First available in Project Euclid: 15 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1329337705

Digital Object Identifier
doi:10.1155/2012/341953

Mathematical Reviews number (MathSciNet)
MR2846451

Zentralblatt MATH identifier
1295.47104

Citation

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


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