<p>In 2010, Victoria Martin Marquez studied a nonexpansive mapping in Hadamard manifolds using Viscosity approximation method. Our goal in this paper is to study the strong convergence of the Viscosity approximation method in Hadamard manifolds. Our results improve and extend the recent research in the framework of Hadamard manifolds.</p>
In this paper, we introduce a Halpern algorithm and a nonconvex combination algorithm to approximate a solution of the split common fixed problem of quasi-
ϕ
-nonexpansive mappings in Banach space. In our algorithms, the norm of linear bounded operator does not need to be known in advance. As the application, we solve a split equilibrium problem in Banach space. Finally, some numerical examples are given to illustrate the main results in this paper and compare the computed results with other ones in the literature. Our results extend and improve some recent ones in the literature.
We study the asymptotic behavior of solutions to a first-order evolution
equation governed by a locally Lipschitz quasi-nonexpansive mapping. We show
that such solutions converge to a fixed point of the quasi-nonexpansive
mapping as time goes to infinity. Time discretization of this system
provides an iterative method to approximate a fixed point of
quasi-nonexpansive mappings on Hadamard manifolds.
In this paper, we propose an iterative algorithm for finding the common
element of solution set of a split equilibrium problem and common fixed
point set of a finite family of asymptotically nonexpansive mappings in
Hilbert space. The strong convergence of this algorithm is proved.
In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.
Strong convergence for nonexpansive mappings by viscosity approximation methods in Hadamard manifolds
