3 CONJECTURES ON SHEPARD INTERPOLATORY OPERATORS

After establishing direct and converse approximation theorems for the Shepard interpolatory operators, J. Szabados (Approx. Theory Appl. 7, No. 3, 1991, 63-76) left some open saturation problems (''the most int riguing questions'' as he said), which he raised as three conjectures. The present paper proves the second parts of some conjectures, but co nstructs counterexamples to show that the first parts of three conject ures are not true. The constructive procedure uses some novel ideas an d techniques. (C) 1998 Academic Press.