Iterative Algorithms for Finding Common Solutions to Variational Inclusion Equilibrium and Fixed Point Problems

Iterative Algorithms for Finding Common Solutions to Variational Inclusion Equilibrium and Fixed Point Problems

The main purpose of this paper is to introduce an explicit iterative algorithm to study the existence problem and the approximation problem of solution to the quadratic minimization problem. Under suitable conditions, some strong convergence theorems for a family of nonexpansive mappings are proved. The results presented in the paper improve and extend the corresponding results announced by som...

Iterative common solutions for monotone inclusion problems, fixed point problems and equilibrium problems

Let H be a real Hilbert space, and let C be a nonempty closed convex subset of H. Let α > 0, and let A be an α-inverse strongly-monotone mapping of C into H. Let T be a generalized hybrid mapping of C into H. Let B andW be maximal monotone operators on H such that the domains of B andW are included in C. Let 0 < k < 1, and let g be a k-contraction of H into itself. Let V be a γ -strongly monoto...

Common Solutions of an Iterative Scheme for Variational Inclusions, Equilibrium Problems, and Fixed Point Problems

We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse stronglymonotonemappings, the set of solutions of an equilibrium problem, and the set of fixed points of a nonexpansive mapping. We obtain a strong convergence theorem for the sequences generated...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

A New Iterative Method for Finding Common Solutions of a System of Equilibrium Problems, Fixed-Point Problems, and Variational Inequalities

and Applied Analysis 3 set of a nonexpansive mapping in a Hilbert space. Let an arbitrary x1 ∈ H, define sequences {xn} and {un} by F ( un, y ) 1 βn 〈 y − un, un − xn 〉 ≥ 0, ∀y ∈ C, xn 1 αnγf xn I − αnB Sun, ∀n ∈ N. 1.6 They proved that under certain appropriate conditions imposed on {αn} and {βn}, the sequences {xn} and {un} generated by 1.6 converge strongly to the unique solution of the vari...