Approximation of the fixed point of the product of two operators in Banach algebras with applications to some functional equations

In this paper, the existence and uniqueness of the fixed point for the product of two nonlinear operator in Banach algebra is discussed. In addition, an approximation method of the fixed point of hybrid nonlinear equations in Banach algebras is established. This method is applied to two interesting different types of functional equations. In addition, to illustrate the applicability of our results we give some numerical examples.