Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups

Strong Convergence Theorems for Asymptotically Nonexpansive Mappings and Asymptotically Nonexpansive Semigroups

A point x ∈ C is a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T ; that is, F(T)= {x ∈ C : Tx = x}. Also, recall that a family S= {T(s) | 0≤ s <∞} of mappings from C into itself is called an asymptotically nonexpansive semigroup on C if it satisfies the following conditions: (i) T(0)x = x for all x ∈ C; (ii) T(s+ t)= T(s)T(t) for all s, t ≥ 0; (iii) there exists ...

Strong Convergence Theorems for Nonexpansive Semigroups without Bochner Integrals

Strong and $Delta$-convergence theorems for total asymptotically nonexpansive mappings in CAT(0)

In this work we use the Noor iteration process for total asymptotically nonexpansive mapping to establish the strong and $Delta$-convergence theorems in the framework of CAT(0) spaces. By doing this, some of the results existing in the current literature  generalize, unify and extend.

Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups

Throughout this paper, letH be a real Hilbert space with inner product 〈·,·〉 and ‖ · ‖. We use xn⇀ x to indicate that the sequence {xn} converges weakly to x. Similarly, xn → x will symbolize strong convergence. we denote by N and R+ the sets of nonnegative integers and nonnegative real numbers, respectively. let C be a closed convex subset of a Hilbert space H , and Let T : C → C be a nonexpan...

Strong Convergence Theorems for a Finite Family of Nonexpansive Mappings

Let H be a real Hilbert space, C a nonempty closed convex subset of H , and T : C → C a mapping. Recall that T is nonexpansive if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. A point x ∈ C is called a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T , that is, F(T) = {x ∈ C : Tx = x}. Recall that a self-mapping f : C → C is a contraction on C, if there exists a constant α∈ (0...