A viscosity hybrid steepest-descent method for a system of equilibrium and fixed point problems for an infinite family of strictly pseudo-contractive mappings

Fixed point iteration for a countable family of multi-valued strictly pseudo-contractive-type mappings

This paper introduces a new averaged algorithm for finding a common fixed point of a countably infinite family of generalized k-strictly pseudocontractive multi-valued mappings. The new iterative sequence introduced is proved to be an approximating fixed point sequence for common fixed points of a countably infinite family of this class of mappings. Furthermore, under some mild assumptions, str...

Viscosity Method for Hierarchical Fixed Point Problems with an Infinite Family of Nonexpansive Nonself-Mappings

for all x ∈ X, whereX denotes the dual space ofX and ⟨⋅, ⋅⟩ the generalized duality pairing between X and X. If X = H is a Hilbert space, then J becomes the identitymapping onH. A point x ∈ C is a fixed point of T : C ⊂ X → X provided Tx = x. Denote by F(T) the set of fixed points of T; that is, F(T) = {x ∈ C : Tx = x}. Let X be a normed linear space with dim X ≥ 2. The modulus of smoothness of...

A New Iterative Method for Solving Equilibrium Problems and Fixed Point Problems for Infinite Family of Nonexpansive Mappings

Hybrid viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many nonexpansive mappings

Recently, Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 2006, doi: 10.1016/j.jmaa.2006.08.036] suggested and analyzed an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set ...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems