A numerical method is proposed to find the approximate element of this common set.
In this paper, motivated by the work of Ceng et al. [18, 20], Yao et al. [12], Bnouhachem [19] and others, we propose an iterative method for finding an approximate element of the common set of solutions of EP (1.1) and HFPP (1.4) in the setting of real Hilbert spaces.
In this paper, motivated by the work of Ceng et al. [5, 21, 24], Al-Mazrooei et al. [2], Yao et al. [15], Bnouhachem [23] and by the recent work going in this direction, we give an iterative method for finding the approximate element of the common set of solutions of (1.1), (1.5), and (1.9) in a real Hilbert space.
The following result can be viewed as an extension and improvement of the method of Yao et al. [27] for finding an approximate element of the common set of solutions of a split equilibrium problem and a hierarchical fixed point problem in a real Hilbert space.
The following result can be viewed as extension and improvement of the method of Yao et al. [20] for finding the approximate element of the common set of solutions of a generalized equilibrium problem and a hierarchical fixed point problem in a real Hilbert space.
In this paper, we suggest and analyze an iterative scheme for finding the approximate element of the common set of solutions of a generalized equilibrium problem, a variational inequality problem and a hierarchical fixed point problem in a real Hilbert space.
If we have the Lipschitzian mapping U = f, F = I, ρ = μ = 1, and A = 0, we obtain an extension and improvement of the method of Yao et al.[12] for finding the approximate element of the common set of solutions of a mixed equilibrium problem and a hierarchical fixed-point problem in a real Hilbert space.
Putting (D=varphi=0), (B_{m}=0) for each m, and (delta_{n}=0) in Algorithm 3.1, we obtain the following result, which can be viewed as an extension and improvement of the method of Bnouhachem et al. [22] for finding the approximate element of the common set of solutions of equilibrium problem and a hierarchical fixed point problem.
Putting γ n = 0 and A = 0 in Algorithm 3.1, we obtain the following result which can be viewed as an extension and improvement of the method of Wang and Xu [30] for finding the approximate element of the common set of solutions of a generalized mixed equilibrium problem and a hierarchical fixed point problem in a real Hilbert space.
Putting U = f, F = I, ρ = μ = 1, γ n = 0, and A = 0, we obtain an extension and improvement of the method of Yao et al. [15] for finding the approximate element of the common set of solutions of a generalized mixed equilibrium problem and a hierarchical fixed point problem in a real Hilbert space.
The proposed method is an extension and improvement of the method of Wang and Xu [42] for finding the approximate element of the common set of solutions of a split equilibrium problem and a hierarchical fixed-point problem in a real Hilbert space.
