| 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. |
