Later on, Ceng and Yao [11] also introduced an extragradient-like approximation method, which is based on the above extragradient method and viscosity approximation method, and proved the strong convergence result under certain conditions.
In this paper, we propose an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities (in short, GSVI) in X based on Korpelevich's extragradient method and viscosity approximation method.
Based on the extragradient method and viscosity approximation method, Yao et al. [8] proposed and analyzed a relaxed extragradient method for finding a common solution of GSVI (1.3) and a fixed point problem of a strictly pseudo-contractive mapping S : C → C. Theorem YLK (see [[8], Theorem 3.2]).
In this paper, considering the problem of solving a system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in Banach spaces, we propose a two-step relaxed extragradient method which is based on Korpelevich's extragradient method and viscosity approximation method.
Here, the two-step relaxed extragradient method is based on Korpelevich's extragradient method [10] and viscosity approximation method.
Based on the extragradient method [33] and viscosity approximation method [23], Yao et al. [26] introduced and studied a relaxed extragradient iterative algorithm for finding a common solution of problem (1.2) and the fixed point problem of a strictly pseudocontraction in a real Hilbert space H. Theorem 1.1.
In the present paper, we mainly propose two different methods, namely, relaxed viscosity method and composite viscosity method, to find a common fixed point of an infinite family of nonexpansive mappings, a system of variational inequalities and zero of an accretive operator in the setting of a uniformly convex and 2-uniformly smooth Banach spaces.
The variation in these properties is related to differences in composition, mixing methods, aging, temperature and viscosity during application.
The resistance of the conductive cement composites was measured by a two-probe method, and the viscosity was evaluated using a rheometer immediately after the mixing process.
The multi-step iterative method in [27] involves the Ishikawa-type iterative method and the viscosity approximation method.
