Iterative algorithm for solving mixed quasi-variational-like inequalities with skew-symmetric terms in Banach spaces

We develop an iterative algorithm for computing the approximate solutions of mixed quasi-variational-like inequality problems with skew-symmetric terms in the setting of reflexive Banach spaces. We use Fan-KKM lemma and concept of η-cocoercivity of a composition mapping to prove the existence and convergence of approximate solutions to the exact solution of mixed quasi-variational-like inequalities with skew-symmetric terms. Furthermore, we derive the posteriori error estimates for approximate solutions under quite mild conditions.