An Explicit Viscosity Iterative Algorithm for Finding Fixed Points of Two Noncommutative Nonexpansive Mappings

Weak Convergence of Mann Iterative Algorithm for two Nonexpansive mappings

The mann fixed point algorithm play an importmant role in the approximation of fixed points of nonexpansive operators. In this paper, by considering new conditions, we prove the weak convergence of mann fixed point algorithm, for finding a common fixed point of two nonexpansive mappings in real Hilbert spaces. This results extend the privious results given by Kanzow and Shehu. Finally, we give ...

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...

Approximating fixed points of generalized nonexpansive mappings

Two-step Iterative Process For Common Fixed Points of Two Asymptotically Quasi-nonexpansive Mappings

In this paper, we consider an iteration process for approximating common fixed points of two asymptotically quasinonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces. Keywords—Asypmtotically quasi-nonexpansive mappings, Common fixed point, Strong and weak convergence, Iteration process.

Iterative Algorithm for Common Fixed Points of Infinite Family of Nonexpansive Mappings in Banach Spaces

Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X, {Tk}k 1 : C → C an infinite family of nonexpansive mappings with the nonempty set of common fixed points ⋂∞ k 1 Fix Tk , and f : C → C a contraction. We introduce an explicit iterative algorithm xn 1 αnf xn 1 − αn Lnxn, where Ln ∑n k 1 ωk/sn Tk, Sn ∑n k 1 ωk, and wk > 0 with ∑∞ k 1 ωk 1. Under certain appropriat...

A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings

Suppose that K is a nonempty closed convex subset of a real uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction. Let T1,T2 : K → E be two weakly inward and asymptotically nonexpansive mappings with respect to P with sequences {Kn},{ln} ⊂ [1,∞), limn→∞kn = 1, limn→∞ln = 1, F(T1)∩ F(T2) = {x ∈ K : T1x = T2x = x} =∅, respectively. Suppose that {xn} is a sequence in...