Uniform convergence of Lagrange interpolation based on the Jacobi nodes

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 of Lambda-variation, Phi-variation, the modulus of variation, and the Banach indicatrix of a function. (C) 1996 Academic Press. Inc.