We consider a regularization method based on the Browder–Tikhonov and iterative regularization method that can be used to find a solution of a class of accretive variational inequalities in a $q$-uniformly smooth Banach space, and the solutions are sought in the set of common fixed points of a countable family of nonexpansive mappings. We also introduce an iteration method, which is implicit and converges strongly, based on the steepest descent method with a strongly accretive and strictly pseudocontractive mapping. Our results generalize and extend some well-known regularization methods in the literature.