SUMMARY
Let E be a uniformly smooth and uniformly convex real Banach space and E* be its dual space. We consider a multivalued mapping A : E ? 2E* which is bounded, generalized F-strongly monotone and such that for all t > 0, the range R(Jp+tA) = E*, where Jp (p > 1) is the generalized duality mapping from E into 2E* . Suppose A-1(0) = Ø, we construct an algorithm which converges strongly to the solution of 0 ? Ax. The result is then applied to the generalized convex optimization problem.