A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings

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 {Ti} m i 1 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 {Ti} m i 1 is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.

Strong convergence theorems for nonlinear operator equations with total quasi-ϕ-asymptotically nonexpansive mappings and applications

“…As an application, we shall utilize our results to study the iterative solutions of the nonlinear Hammerstian type equation. The results presented in the article improve and extend the corresponding results in [1][2][3][4][5][7][8][9][10][11][12][13][14][15][16].…”

Multiple-set split feasibility problems for total asymptotically strict pseudocontractions mappings

“…The class of mapping was introduced by Alber et al [4]. From the definition, we see that the class of total asymptotically nonexpansive mappings includes the class of asymptotically nonexpansive mappings as special cases, see [5,6] for more details.…”

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.…”