Family Of Demicontractive Mappings Research Articles

A New Iterative Algorithm for Pseudomonotone Equilibrium Problem and a Finite Family of Demicontractive Mappings

In this paper, we introduce a new iterative method in a real Hilbert space for approximating a point in the solution set of a pseudomonotone equilibrium problem which is a common fixed point of a finite family of demicontractive mappings. Our result does not require that we impose the condition that the sum of the control sequences used in the finite convex combination is equal to 1. Furthermore, we state and prove a strong convergence result and give some numerical experiments to demonstrate the efficiency and applicability of our iterative method.

General iterative method for solving fixed point problems involving a finite family of demicontractive mappings in Banach spaces

The purpose of this paper is to study the general iterative method for demicontractive mappings in Banach spaces. The method gives us a~strong convergence iteration for a~finite family of demicontractive mappings and also permits us to solve variational inequality problems involving accretive operators without any compactness condition. Finally, we provide some applications, and an illustration of the proposed method is given in \(l_4\) spaces. Our results improve many recent results using the general iterative method for finding the fixed points of nonlinear operators.

Parallel Algorithms for Solving a Class of Variational Inequalities over the Common Fixed Points Set of a Finite Family of Demicontractive Mappings

We propose parallel algorithms for solving a class of variational inequalities over the set of common fixed points for a finite family of demicontractive mappings in real Hilbert spaces. Under some suitable conditions, we prove that the sequence generated by the proposed algorithms converges strongly to a solution of the problem. We apply the proposed algorithms to strongly monotone variational inequality problems with pseudomonotone equilibrium constraints by defining a quasi-nonexpansive and demi-closed mapping whose fixed point set coincides with the solution set of the equilibrium problem.

The split common fixed point problem for infinite families of demicontractive mappings

In this paper, we propose a new algorithm for solving the split common fixed point problem for infinite families of demicontractive mappings. Strong convergence of the proposed method is established under suitable control conditions. We apply our main results to study the split common null point problem, the split variational inequality problem, and the split equilibrium problem in the framework of a real Hilbert space. A numerical example supporting our main result is also given.

Solving split equality common fixed point problem for infinite families of demicontractive mappings

In this paper, we consider the split equality common fixed point problem of infinite families of demicontractive mappings in Hilbert spaces. We introduce a simultaneous iterative algorithm for solving the split equality common fixed point problem of infinite families of demicontractive mappings and prove a strong convergence of the proposed algorithm under some control conditions.

A hybrid shrinking projection method for common fixed points of a finite family of demicontractive mappings with variational inequality problems

In this article, we prove some properties of a demicontractive mapping defined on a nonempty closed convex subset of a Hilbert space. By using these properties, we obtain strong convergence theorems of a hybrid shrinking projection method for finding a common element of the set of common fixed points of a finite family of demicontractive mappings and the set of common solutions of a finite family of variational inequality problems in a Hilbert space. A numerical example is presented to illustrate the proposed method and convergence result. Our results improve and extend the corresponding results existing in the literature.

Split Common Null Point and Common Fixed Point Problems Between Banach Spaces and Hilbert Spaces

In this paper, we present a new algorithm for solving the split common null point and the common fixed point problems between Banach spaces and Hilbert spaces, to find a point which belongs to the common zero point set of a finite family of maximal monotone operators and the common fixed point set of a finite family of demicontractive mappings in a Hilbert space such that its image under a linear transformation belongs to the common zero point set of another finite family of maximal monotone operators in a Banach space. We prove that the sequence generated by the proposed algorithm converges strongly to a common solution of the split common null point and the common fixed point problems, which is also an unique solution of a variational inequality as an optimality condition for a minimization problem.

General algorithms for split common fixed point problem of demicontractive mappings

In the first part of this paper, we present a new general algorithm for solving the split common fixed point problem for an infinite family of demicontractive mappings. We establish strong convergence of the algorithm in an infinite dimensional Hilbert space. As applications, we consider algorithms for split variational inequality problem and split common null point problem. In the second part of this paper, we present a new algorithm and strong convergence theorem for approximation of solutions of split equality fixed point problems for an infinite family of demicontractive mappings. Our results improve and generalize some recent results in the literature.

A new algorithm for two finite families of demicontractive mappings and equilibrium problems

In this paper, we introduce a new algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of two finite families of demicontractive mappings. The strong convergence theorem of the proposed algorithm is established under some suitable control conditions in a real Hilbert space. Our result generalizes several recent results in the current literature.