Let X, Y be Banach spaces, D ⊂ X be convex, F : D ⊂ X → Y be a Fréchet differentiable operator. We shall determine a solution x of the equation F(x) = 0, Many problems from Applied Sciences can be solved finding the solutions of equations in a form like (6.1) [5, 9, 12, 13, 27, 31-33].