On Two Conjectures of M.Hasson
Received:April 29, 1983  
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Xu Shusheng 江南大学 
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      Let ‖?‖[α,b] be the supremum norm in C[α,b] .By Πn we denote the collection of all algebraic polynomials of degree at most n. For positive integer k and n≥k, let Πnk be the collection of all polynomials which are of degree at most n, and restricted not to contain the power xk of x. If f∈C[α,b] . then we define En(f)=inf(‖f-pn[α,b]:pn∈Πn). and Enk(f)=inf(‖f-qn[α,b]:qn∈Πnk). we assume that f(x) is not a polynomial, and therefore En(f)≠0.
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