Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings

Abstract

In this work we prove a new strong convergence result of the regularized successive approximation method given bywhere lim n→∞ q n = 0 andfor T a total asymptotically nonexpansive mapping, i.e., T is such thatwhere k 1 n and k 2 n are real null convergent sequences and φ : R + → R + is continuous and such that φ(0) = 0 and lim t→∞ φ(t) t ≤ C for a certain constant C > 0. Among other features, our results essentially generalize existing results on strong convergence for T nonexpansive and asymptotically nonexpansive. The convergence and stability analysis is given for both self-and nonself-mappings.Running title: Strong convergence to fixed points

Hybrid algorithm with perturbations for total asymptotically non-expansive mappings in CAT(0) space

“…It is called the CR iterative scheme. If we take α n = 0 the iterative process (3) reduces to S-iteration (2).…”

“…They [3] further studied the iterative approximation of fixed point for total asymptotically nonexpansive mappings using a modified Krasnoselskii-Mann iteration process. Iterative approximation of fixed points of total asymptotically non-expansive mappings has also been studied by [2,13,14,19].…”

Strong Convergence Theorems for Two Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

“…Recently, many authors improved and generalized the results of Halpern [11] by means of different methods; see, for example, [2,4,10,[12][13][14][15][16][17] and the references therein. In general, there are two ways as follows.…”

“…Motivated and inspired by [2,4,10,[12][13][14][15][16][17], the purpose of this paper is to modify Halpern iteration (2) by means of both methods above for two total quasi--asymptotically nonexpansive mappings and then to prove the strong convergence in the framework of Banach spaces. The results presented in this paper extend and improve the corresponding results of Martinez-Yanes and Xu [15], Plubtieng and Ungchittrakool [16], Qin et al [17], and others.…”

The Split Common Fixed Point Problem for a Family of Multivalued Quasinonexpansive Mappings and Totally Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces

“…[25] Let {λ n } and {γ n } be nonnegative and {α n } be positive real numbers, such that λ n+1 ≤ λ n − α n λ n + γ n , n ≥ 0. Let for all n > 1,…”