Abstract: To solve Fredholm integral equations of the second kind, a generalized linear functional was introduced and then function-valued Padé-type approximation was defined. Some useful identities are established by means of error formulas for function-valued Padé-type approximation. A recursive algorithm is also constructed. An example is given to show effectiveness of this method.

Key words: functional valued, Padé-type approximation, identities, recursive algorithm, Fredholm integral equations.