Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions. (19th May 2008)

• Record Type: Journal Article
• Authors: Hu, Liang-Gen; Xiao, Ti-Jun; Liang, Jin
• Other Names: Ben-El-Mechaiekh Hichem Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2008(2008)
• Publication Date: 2008-05-19
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2008/824607
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed point. As one will see, we derive these strong convergence theorems in uniformly convex Banach spaces and without any requirement of the compactness on the domain of the mapping. The results given in this paper extend some previous theorems.