In this paper, we suggest and analyze an iterative method for finding the approximate element of the common set of solutions of (1.1), (1.9 - 1.10), and (1.11) in real Hilbert space, which can be viewed as a refinement and improvement of some existing methods for solving a system of variational inequality problem, a split equilibrium problem, and a hierarchical fixed-point problem.
In this paper, we study a hybrid split problem (HSP for short) for equilibrium problems and fixed point problems of nonlinear operators.
In this paper, motivated by the problems (EP) and (FTEP), we study the following mathematical model about a hybrid split problem for equilibrium problems and fixed point problems of nonlinear operators (HSP for short).
The mathematical model about a hybrid split problem for equilibrium problems and fixed point problems of nonlinear operators (HSP for short) is defined as follows: Find p ∈ C such that T p = p, f ( p, y ) ≥ 0, ∀ y ∈ C, and u : = A p satisfying S u = u ∈ K, g ( u, v ) ≥ 0, ∀ v ∈ K. (HSP).
Later, in 2013, Kazmi and Rizvi [20] considered the iterative method to compute the common approximate solution of a split equilibrium problem, a variational inequality problem and a fixed point problem for a nonexpansive mapping in the framework of real Hilbert spaces.
In this paper, we suggest and analyze an iterative scheme for finding an approximate element of the common set of solutions of a split equilibrium problem, a variational inequality problem and a hierarchical fixed point problem in a real Hilbert space.
Thus, we can use condition (2.5) to replace the Lipschitz assumption of pseudo-contractive mappings when we study a split feasibility problem or other problems involved in pseudo-contractive mappings.
As applications, we consider the algorithms for a split feasibility problem and a split optimization problem and give strong convergence theorems for these problems in Hilbert spaces.
As applications, we consider algorithms for a split feasibility problem and a split optimization problem and give strong convergence theorems for these problems in Hilbert spaces.
