A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces

We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given

The Hybrid Projection Methods for Pseudocontractive, Nonexpansive Semigroup, and Monotone Mapping

We modify the three-step iterative schemes to prove the strong convergence theorems by using the hybrid projection methods for finding a common element of the set of solutions of fixed points for a pseudocontractive mapping and a nonexpansive semigroup mapping and the set of solutions of a variational inequality problem for a monotone mapping in a Hilbert space under some appropriate control conditions. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings

On some Mann's type iterative algorithms

AbstractFirst we present some interesting variants of Mann's method. In the last section, we show that many existing results in the literature are concrete realizations of our general scheme under varying assumptions on the coefficients

Implicit Mann approximation with perturbations for nonexpansive semigroups in CAT(0) spaces

Author name used in this publication: Tsz-leung Yip2012-2013 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe