Iterative Methods for Pseudocontractive Mappings in Banach Spaces. (27th March 2013)

• Record Type: Journal Article
• Authors: Jung, Jong Soo
• Other Names: Song Yisheng Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-03-27
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/643602
• Languages: English
• ISSNs: 1085-3375

Abstract

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 .