Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property
In this paper, the convergence results of [V. Berinde; A convergence theorem for Mann iteration in the class of Zamfirescu operators, Analele Universitatii de Vest, Timisoara, Seria Matematica-Informatica 45 (1) (2007), 33–41], [V. Berinde; On the convergence of Mann iteration for a class of quasi-contractive operators, Preprint, North University of Baia Mare (2003)] and [V. Berinde; On the Convergence of the Ishikawa Iteration in the Class of Quasi-contractive Operators, Acta Math. Univ. Comenianae...
The aim of this paper is to propose two modified forward-backward splitting algorithms for zeros of the sum of a maximal monotone operator and a Bregman inverse strongly monotone operator in reflexive Banach spaces. We prove weak and strong convergence theorems of the generated sequences by the proposed methods under some suitable conditions. We apply our results to study the variational inequality problem and the equilibrium problem. Finally, a numerical example is given to illustrate the proposed...
In this article we modify an iteration process to prove strong convergence and Δ- convergence theorems for a finite family of nonexpansive multivalued mappings in hyperbolic spaces. The results presented here extend some existing results in the literature.
In this paper, weak and strong convergence of finite step iteration sequences to a common fixed point for a pair of a finite family of nonexpansive mappings and a finite family of asymptotically nonexpansive mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented.