A viscosity approximation method for nonself operators and equilibrium problems in Hilbert spaces

A viscosity approximation method for nonself operators and equilibrium problems in Hilbert spaces

Viscosity approximate methods have recently received much attention due to the applications in convex optimization problems. In this paper, we study a viscosity iterative algorithm with computational errors. Strong convergence theorems of solutions are established in the framework of Hilbert spaces. The main results presented in this paper improve the corresponding results announced recently. c...

Viscosity Approximation Methods for Nonexpansive Nonself-Mappings in Hilbert Spaces

Viscosity approximation methods for nonexpansive nonself-mappings are studied. Let C be a nonempty closed convex subset of Hilbert space H , P a metric projection of H onto C and let T be a nonexpansive nonself-mapping from C into H . For a contraction f on C and {tn} ⊆ (0,1), let xn be the unique fixed point of the contraction x → tn f (x) + (1− tn)(1/n) ∑n j=1(PT) x. Consider also the iterati...

A Viscosity Approximation Method for Finding Common Solutions of Variational Inclusions, Equilibrium Problems, and Fixed Point Problems in Hilbert Spaces

We introduce an iterative method for finding a common element of the set of common fixed points of a countable family of nonexpansivemappings, the set of solutions of a variational inclusion with set-valued maximal monotone mapping, and inverse strongly monotone mappings and the set of solutions of an equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theo...

Viscosity Approximation Methods for Equilibrium Problems, Variational Inequality Problems of Infinitely Strict Pseudocontractions in Hilbert Spaces

Viscosity Approximation Methods for Equilibrium Problems and Zeroes of an Accretive Operator in Hilbert Spaces

In this paper, we establish a composite iteration scheme by the viscosity approximation method for finding a common element of the set of zero points of an accretive operator and the set of solutions of an equilibrium problem in the framework of a Hilbert space. Mathematics Subject Classification: 39B12, 47H06, 47H10