Extragradient Methods for Solving Equilibrium Problems,Variational Inequalities,and Fixed Point Problems

In this paper, we propose the new extragradient algorithms for an α-inverse-strongly monotone operator and a relatively nonexpansive mapping in Banach spaces. We prove convergence theorems by this methods under suitable conditions. Applying our algorithms, we find a zero paint of maximal monotone operators. Using FMINCON optimization toolbox in MATLAB, we give an example to illustrate the usability of our results.