Summary: In this paper, we prove some fixed point theorems in vector algebra Banach spaces. We establish versions of Perov, Schauder and Krasnosel’skki type fixed point theorem for the sum of a contraction operator and a compact operator. The obtained results are applied to prove some theorems on the existence of solutions to nonlinear integral equations in Banach algebras. Finally, some examples are given to illustrate the result.