Iterative Methods for Equilibrium Problems and Monotone Inclusion Problems in Hilbert Spaces

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

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...

A general inexact iterative method for monotone operators, equilibrium problems and fıxed point problems of semigroups in Hilbert spaces

Let H be a real Hilbert space. Consider on H a nonexpansive family T = {T(t) : 0 ≤ t < ∞} with a common fixed point, a contraction f with the coefficient 0 0. Assume that 0 < γ < γ̄ /α and that S = {S (t) : 0 ≤ t < ∞} is a family of nonexpansive self-mappings on H such that F(T ) ⊆ F(S) and T has prop...

General Iterative Methods for Equilibrium Problems and Infinitely Many Strict Pseudocontractions in Hilbert Spaces

We propose an implicit iterative scheme and an explicit iterative scheme for finding a common element of the set of fixed point of infinitely many strict pseudocontractive mappings and the set of solutions of an equilibrium problem by the general iterative methods. In the setting of real Hilbert spaces, strong convergence theorems are proved. Our results improve and extend the corresponding res...

A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

We introduce a general iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Our results improve and extend the corresponding ones announced by S. Takahashi and W. Takahashi in 2007, Marino and Xu in 2006, Combettes and Hirstoaga in 2005, and ...