The existence of solutions of operator equations in Fréchet Algebras and applications

The paper examines fixed point outcomes for the two-variable operator F acting in Fréchet algebras. These results can be viewed as modifications of the fixed point theorem for the \(C+AB\) $C+AB$ operator within a wider context. Through our primary findings, we can establish the existence of solutions for nonlinear integral equations with deviations that are not bounded. The proofing technique employed also allows for an added description of the asymptotic stability of the solutions of the relevant equation.