Abstract and Applied Analysis

Iterative Methods for Pseudocontractive Mappings in Banach Spaces

Jong Soo Jung

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Abstract

Let E a reflexive Banach space having a uniformly Gâteaux differentiable norm. Let C be a nonempty closed convex subset of E , T : C C a continuous pseudocontractive mapping with F ( T ) , and A : C C a continuous bounded strongly pseudocontractive mapping with a pseudocontractive constant k ( 0,1 ) . Let { α n } and { β n } be sequences in ( 0,1 ) satisfying suitable conditions and for arbitrary initial value x 0 C , let the sequence { x n } be generated by x n = α n A x n + β n x n - 1 + ( 1 - α n - β n ) T x n ,   n 1 . If either every weakly compact convex subset of E has the fixed point property for nonexpansive mappings or E is strictly convex, then { x n } converges strongly to a fixed point of T , which solves a certain variational inequality related to A .

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 643602, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393444403

Digital Object Identifier
doi:10.1155/2013/643602

Mathematical Reviews number (MathSciNet)
MR3039129

Zentralblatt MATH identifier
06209386

Citation

Jung, Jong Soo. Iterative Methods for Pseudocontractive Mappings in Banach Spaces. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 643602, 7 pages. doi:10.1155/2013/643602. https://projecteuclid.org/euclid.aaa/1393444403


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