Alternatively, the problem of finding a common fixed point of a sequence of finite self-mappings { S i } i = 1 N ( N ≥ 1 ) is described as follows: Find x ∗ ∈ C such that.
The purpose of this paper is to prove a strong convergence theorem of an iterative scheme associated to a strongly nonexpansive sequence for finding a common element of the set of equilibrium problems and the set of fixed point problems of a pair of sequences of nonexpansive mappings where one of them is a strongly nonexpansive sequence.
Very recently, Aoyama et al. [22] introduce a Halpern type iterative sequence for finding a common fixed point of a countable family of nonexpansive mappings.
Recently, for the sequence of nonexpansive mappings with some special conditions, Aoyama et al. [3] introduced a Halpern type iterative sequence for finding a common fixed point of a countable family of nonexpansive mappings satisfying some conditions.
We introduce a new iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space.
We introduce two iterative sequence for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of strict pseudocontractions in Hilbert Space.
In this paper we prove the strong convergence of an iterative sequence for finding a common element of the fixed points set of a strictly pseudocontractive mapping and the solution set of the constrained convex minimization problem for a convex and continuously Fréchet differentiable functional in a real Hilbert space.
The purpose of this paper is to consider the weak convergence of an iterative sequence for finding a common element in the set of solutions of generalized equilibrium problems, in the set of solutions of classical variational inequalities, and in the set of fixed points of nonexpansive mappings.
In 2008, Plubtieng and Punpaeng [7] introduced a new iterative sequence for finding a common element of the set of solution of equilibrium problems and the set of fixed points of a nonexpansive mapping in a Hilbert space which is the optimality condition for the minimization problem.
In this paper, thanks to the condition introduced by Aoyama et al. [5], We introduce two iterative sequence for finding a common element of the set of solutions of an equilibrium problems and the set of fixed points of a countable family of strict pseudocontractions mappings in Hilbert Space.
