The purpose of this paper is to analyze the convergence of the iterative methods for mixed variational inequalities with convex nondifferentiable functionals and J-pseudomonotone, J-potential and J-coercive operators in real uniformly smooth Banach spaces. Such inequalities arise, in particular, in descriptions of stabilized filtration and equilibrium problems for soft shells. Our results extend some results of [1] from real Hilbert spaces to real uniformly smooth Banach spaces with modulus of smoothness of power type q>1 which admit a weakly sequentially continuous duality map.