We prove that certain two-point Padé approximants occupying the diagonal of the Padé table form monotone sequences of lower and upper bounds uniformly converging to a Stieltjes function. The results can be applied to the theory of inhomogeneous media for the calculation of the bounds on the effective transport coefficients of heterogeneous materials.
- AMS subject classification: 41A21, 41A25, 73K20
- Continued fractions
- Padé approximants
- effective conductivity