Abstract. We obtain and substantiate the generalization of continued Thiele-type fractions for the interpolation of nonlinear operators acting from a linear topological space X into an algebra Y with a unit I. We show that the interpolation continued Thiele-type fractions for vector-valued and matrix-valued functions and those for functionals of many variables can be deduced from such a generalization as its important special cases.

Keywords: continued Thiele-type fraction, interpolation, nonlinear operator, continual nods.