MSGEP is a generalization of the generalized equilibrium problem, the split equilibrium problem and the split variational inequality problem.
In this paper, we propose an iterative algorithm to find the common solution of the generalized equilibrium problem, variational inequality problem, and fixed point problem for a relatively nonexpansive mapping in a real Banach space.
Motivated by these results, we investigated the common element problems of the generalized equilibrium problem (2.1) and quasi-nonexpansive mappings based on the shrinking projection algorithm.
Inspired by the work of Takahashi and Takahashi [2], and Ceng et al. [3], Ceng et al. [4] introduced and analyzed an iterative scheme for finding the approximate solutions of the generalized equilibrium problem (1.2), a system of general generalized equilibrium problems (1.1) and a fixed point problem of a nonexpansive mapping in a Hilbert space.
By using our main result, Theorem 3.4 reduces to the Corollary 3.6, the solution of the generalized equilibrium problem and Corollary 3.7, the split equilibrium problem.
In this section, we suggest and analyze our method for finding the common solutions of the system of the generalized equilibrium problem (1.1) and the hierarchical fixed point problem (1.6).
Next, we give some special cases of the generalized equilibrium problem (2.2). (I) If F ≡ 0, then problem (2.2) is reduced to the classical variational inequality (2.1).
We discover the stability of the generalized Riemann problem, but do not observe the composite wave, which motivates us to consider the related problems including the coupling of two different hyperbolic systems.
Toro, V.A. Titarev, Solution of the generalized Riemann problem for advection reaction equations, Proc.
