On generalized extragradient implicit method for systems of variational inequalities with constraints of variational inclusion and fixed point problems

Abstract

In a real Banach space, let the VI indicate a variational inclusion for two accretive operators and let the CFPP denote a common fixed point problem of countably many nonexpansive mappings. In this article, we introduce a generalized extragradient implicit method for solving a general system of variational inequalities (GSVI) with the VI and CFPP constraints. Strong convergence of the suggested method to a solution of the GSVI with the VI and CFPP constraints under some suitable assumptions is established.

A Bregman hybrid extragradient method for solving pseudomonotone equilibrium and fixed point problems

“…The EP can be considered as a general model and covers numerous fascinating and complicated problems in nonlinear analysis, such as fixed point problems, variational inequalities, and Nash equilibrium problems; see, e.g., [4,16]. It is known that several problems arising in mathematics, economics, physics, computer science, and management science, can be modeled as an EP, and many fixed point methods have been investigated for the EP; see, e.g., [5,9,12,15,25] for details.…”