2010/05/27 by Farrukh Mukhamedov, Mukhamedov, Farrukh, Mansoor Saburov +1
Computer Science · Mathematics · #46B20 #46N10 #47H09 #47H10 #Advanced Optimization Algorithms Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Numerical Analysis (math.NA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1005.5072
openalex publication_date 2010/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we unify all know iterative methods by introducing a new\nexplicit iterative scheme for approximation of common fixed points of finite\nfamilies of total asymptotically I-nonexpansive mappings. Note that such a\nscheme contains as a particular case of the method introduced in [C.E. Chidume,\nE.U. Ofoedu, \Inter. J. Math. & Math. Sci. \2009(2009) Article\nID 615107, 17p]. We construct examples of total asymptotically nonexpansive\nmappings which are not asymptotically nonexpansive. Note that no such kind of\nexamples were known in the literature. We prove the strong convergence theorems\nfor such iterative process to a common fixed point of the finite family of\ntotal asymptotically I-nonexpansive and total asymptotically nonexpansive\nmappings, defined on a nonempty closed convex subset of uniformly convex Banach\nspaces. Moreover, our results extend and unify all known results.\n