Strong Convergence to Common Fixed Points of Countable Relatively Quasi-Nonexpansive Mappings

Strong Convergence Theorems of Common Fixed Points for a Family of Quasi--Nonexpansive Mappings

Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

Strong Convergence to Common Fixed Points of a Finite Family of Nonexpansive Mappings

Let C be a closed convex subset of a Banach space E. A mapping T of C into itself is called nonexpansive if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F(T) the set of fixed points of T . Let T1,T2, . . . ,Tr be a finite family of nonexpansive mappings satisfying that the set F =⋂i=1F(Ti) of common fixed points of T1,T2, . . . ,Tr is nonempty. The problem of finding a common fixed point has...

Strong Convergence to Common Fixed Points of Nonexpansive Mappings without Commutativity Assumption

for each x, y ∈ C. For a mapping T of C into itself, we denote by F(T) the set of fixed points of T . We also denote by N and R+ the set of positive integers and nonnegative real numbers, respectively. Baillon [1] proved the first nonlinear ergodic theorem. Let C be a nonempty bounded convex closed subset of a Hilbert spaceH and let T be a nonexpansive mapping of C into itself. Then, for an arb...

Convergence to common fixed points for generalized asymptotically quasi-nonexpansive mappings

The aim of this article is to establish some strong convergence theorems of three-step iteration process with errors for approximating common fixed point for generalized asymptotically quasi-nonexpansive mappings and also establish a weak convergence theorem by using Opial’s [11] condition for said iteration scheme and mappings in the framework of Banach spaces. The results presented in this pa...