A modification of Extragradient method for solving fixed point, variational inequality, and equilibrium problems without the monotonicity

Thidaporn Seangwattana

Abstract

The propose of this work is to modify an Extragradient method (in [2]) for finding a common solution of fixed point, variational inequality,  and equilibrium problems without the monotone assumption of a bifunction in a Hilbert space. A weak convergence theorem is presented by the proposed method. When reducing some mappings in the method, it can find solutions of various problems without the monotonicity of a bifunction.