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.