Uniform Convergence of Lagrange Interpolation Based on the Jacobi Nodes Original Research Article

Necessary and sufficient conditions are obtained for a continuous function guaranteeing the uniform convergence on the whole interval [−1, 1] of its Lagrange interpolant based on the Jacobi nodes. The conditions are in terms ofΛ-variation,PHgr;-variation, the modulus of variation, and the Banach indicatrix of a function.