a general approach to define the adjoint of non-linear operators in hilbert space

In this paper we have endeavored to indicate a general approach for the adjoint of non-linear operators. for this purpose, we have changed the classical definition of linear operators in the textbooks. then we have obtained the adjoint of these operators with respect to the definition of the derivative an operator or ''frechet derivative''. regarding to definition of the adjoint of anti-linear operators, we have shown a general definition for the adjoint of non-linear operators. our approach works for all of the differentiable operator.