S -matrix inverse scattering problem via the fixed-point theorem

By use of the contraction mapping principle we show explicitly that the equations for the inverse scattering problem (i.e., constructing the full amplitude, A (s,t), from just the s-wave amplitude A/sub 0/(s) given at all real s) in nonrelativistic S-matrix theory have a locally unique solution when there are no pole terms and no subtractions and when the relevant norms are sufficiently small. The corresponding mapping problem for the relativistic, crossing-symmetric case is also formulated and the question of uniqueness is discussed.