The subgradient extragradient method for solving mixed equilibrium problems and fixed point problems in Hilbert spaces

Abstract

In this paper, we introduce an iterative method based on hybrid methods and hybrid extragradient methods for finding a common solution of mixed equilibrium problems and fixed point problems of nonexpansive mappings in a real Hilbert space. We define the notion of generalized skew-symmetric bifunctions which is a natural extension of a skew-symmetric bifunctions. Further, we prove that the sequences generated by the proposed iterative scheme converge strongly to a common solution of these systems. The results presented in this paper are the supplements, extensions and generalizations of the previously known results in this area.