Some Extragradient Methods for Solving Variational Inequalities Using Bregman Projection and Fixed Point Techniques in Reflexive Banach Spaces

In this chapter, we introduce some extragradient methods for solving variational inequalities using Bregman projections and a fixed point technique in reflexive Banach spaces. These algorithms are extensions of the prototypes which have been studied extensively in real Hilbert and 2-uniformly convex Banach spaces. We emphasize that there are some applicable examples (most especially in mechanics) which can be modelled as variational inequalities in reflexive Banach spaces outside Hilbert and 2-uniformly convex Banach spaces. Moreover, the usage of Bregman projections allows the consideration of more general structures of the feasible set. The convergence analysis of the algorithms are given using Bregman distance and fixed point techniques. More so, we present some computational examples to illustrate the effects of various type of convex functions on the proposed algorithm.