A fixed point approach to the Green's functions of Φ24: Local existence of the Borel transforms

We prove the existence at small μ of a unique solution of the system $\text{B =}\text{M}\text{(B)}$ to be satisfied by the set of Borel transformed euclidean Green's functions of a Φ₂⁴ theory, μ being the Borel conjugate variable of the coupling λ. As a byproduct, a new proof of convergence of the Borel transformed perturbative series is obtained.