We recall some of our earlier results on the construction of a mapping defined implicitly, without using the implicit function theorem.All these considerations work in a&d ej-123 the real case, for functions and operators.Then we consider the complex case, proving the analyticity of the function defined implicitly, under certain hypothesis.Some consequences are given.An approximating formula for the analytic form of the solution is also given.
Finally, one illustrates the preceding results by an hogwarts legacy grab application to a concrete functional and operatorial equation.Some related examples are given.