On certain rational interpolatory operators (Q1089860)

Recently \textit{O. Kis} and \textit{J. Szabados} [ibid. 239-260 (1986)] introduced a de la Vallée-Poussin type kernel depending on four parameters (j,k,\(\ell\) and m) and the associated trigonometric and algebraic approximating operators. For suitable combinations of these parameters, they proved Jackson, Timan and Telyakowski-Gopenganz type theorems. In the present paper the authors extend this plan to certain trigonometric and algebraic rational interpolants. They obtain error bounds and order of approximation for their operators. These operators are also interpolatory and have fairly good approximating properties not only orderwise but also with respect to the constants involved.