A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings. (15th December 2009)

• Record Type: Journal Article
• Authors: Chidume, C. E.; Ofoedu, E. U.
• Other Names: Popescu Gelu Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2009(2009)
• Publication Date: 2009-12-15
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2009/615107
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : Let E be a real Banach space, and K a closed convex nonempty subset of E . Let T 1, T 2, …, T m : K → K be m total asymptotically nonexpansive mappings. A simple iterative sequence { x n } n ≥ 1 is constructed in E and necessary and sufficient conditions for this sequence to converge to a common fixed point of { T i } i = 1 m are given. Furthermore, in the case that E is a uniformly convex real Banach space, strong convergence of the sequence { x n } n = 1 ∞ to a common fixed point of the family { T i } i = 1 m is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.