RANGES OF OPERATORS AND NUMERIICAL METHODS FOR IINTEGRAL EQUATIIONS

In this talk we deal with the problem of finding numerical schemes to determine approximately the preimage of an element that lies in the range of a continuous operator between Banach spaces. Depending on whether the operator is linear or not, several methods based on analytical tools —going from a very recent version of the Hahn-Banach theorem to classical results in fixed point theory— are developed. The passage from the theoretical setting to its numerical realization is done by means of the use of bases in adequate spaces, deriving Galerkin and iterative algorithms. Such methods apply to solve numerically some kinds of integral equations.