<p>We consider the problem of approximating the functions that are defined on the interval [ – 1; 1] and satisfying the Lipschitz condition on it, by their operators of the Jacobi–Poisson type, constructed according to the system of orthogonal Jacobi polynomials. In particular, at each point x of the interval [ – 1; 1], integral representations are established for the exact upper bounds of deviations of the Jacobi–Poisson operators from functions of the class Lip_{[ – 1; 1]}α for all 0&lt; α ≤ 1. Solving many problems in the theory of function approximation and system analysis ultimately reduces to the analysis of certain integral representations of the corresponding quantities. The integral representations of the exact upper bounds of deviations of the Jacobi–Poisson operators from functions of the Lipschitz class have been established.</p>