Approximation of common fixed points for finite families of nonself asymptotically nonexpansive mappings in Banach spaces

Abstract

Let E be a real uniformly convex Banach space, K be a closed convex nonempty subset of E which is also a nonexpansive retract with retraction P . Let T 1 , T 2 , . . . , T m : K → E be asymptotically nonexpansive mappings of K into E with sequences (respectively) {k in } ∞ n=1 satisfying k in → 1 as n → ∞, i = 1, 2, . . . , m,. . , m} (respectively). Let {x n } be a sequence generated for m 2 byLet m i=1 F (T i ) = ∅. Strong and weak convergence of the sequence {x n } to a common fixed point of the. . , T m are nonexpansive mappings and the dual E * of E satisfies the Kadec-Klee property, weak convergence theorem is also proved.

A generalization and improvement of Chidume theorems for total asymptotically nonexpansive mappings in Banach spaces

“…As well as a sufficient condition for convergence of the iteration process to a common fixed point of mappings under the setting of uniformly convex Banach space is also established. The results presented in the article not only generalize and improve the corresponding results of Chidume et al [13][14][15] but also unify, extend and generalize the corresponding result of [3][4][5][6][7][9][10][11][12]19]. …”

“…Within the past 30 years, research on iterative approximation of common fixed points of nonexpansive mappings, asymptotically nonexpansive mappings and asymptotically quasi-nonexpansive mappings have been considered by many authors (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and the references therein).…”

A Novel Iterative Algorithm Applied to Totally Asymptotically Nonexpansive Mappings in CAT(0) Spaces

“…Then Alber et al [13] introduced the class of totally asymptotically nonexpansive mappings that generalizes several classes of maps that are extensions of asymptotically nonexpansive mappings. These classes of maps were extensively studied by several authors (see, e.g., [14][15][16][17][18][19], to list just a few). We remark that according to the Example 1 of [20], the class of totally asymptotically nonexpansive mappings properly contains the class of asymptotically nonexpansive mappings.…”

Convergece Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings

“…Iterative methods for approximating fixed points of nonexpansive mappings and their generalisations have been studied by numerous authors (see, e.g., [1][2][3][4][5][6][7][8][9] and the references contained therein).…”