Forcing strong convergence of Korpelevich’s method in Banach spaces with its applications in game theory

We develop a variant of Korpelevich’s method for solving variational inequality problems with pseudomonotone operators in Banach spaces. We establish the strong convergence of the sequence generated by the method under reasonable assumptions on the problem data. Finally, we justify the motivation of our theory by including compelling examples of infinite dimensional variational inequality problems for which our method is applicable.