INEQUALITIES FOR 2-POINT PADE APPROXIMANTS TO THE EXPANSIONS OF STIELTJES FUNCTIONS IN A REAL DOMAIN

General inequalities satisfied in real domain by two-point Pade approx imants (2PPA) to two formal power expansions of Stieltjes functions ha ve been derived. The obtained formulae: (i) generalize the existing in equalities for one-point Pade approximants, (ii) extend the validity o f the inequalities reported in J. Comp. Appl. Math. 67 (1996), 59-72, from the particular case 0 less than or equal to k less than or equal to 2 to the general case 0 less than or equal to k less than or equal to infinity, where k denotes a given number of coefficients of a power expansion of Stieltjes functions at infinity, (iii) clarify the prope rties of 2PPA estimations of the effective conductivity for regular co mposites.