By using a special multipoint continued fraction technique we derive, starting from the truncated power expansions given at a number of discrete real points, the general inequalities for the effective transport coefficients Q of macroscopically isotropic two phase media. The inequalities obtained provide new upper and lower bounds on Q$,$ the best ones with respect to rational functions and the available power series coefficients. In particular cases these new bounds reduce to the classical ones of Wienner and Hashin-Shtrikman. They also coincide with the estimations due to Milton and Bergman obtained for the fitting problem. Many illustrative examples clearly show the usefulness of the new bounds derived.