Critical fixed point theorems in Banach algebras under weak topology features

In this paper, we establish some new critical fixed point theorems for the sum AB + C in a Banach algebra relative to the weak topology, where I−C/A is allowed to be non invertible. In addition, a special class of Banach algebras will be considered. As an application, our results are used to prove the existence of solutions for a nonlinear integral equation.