摘要
Let the set of generalized polynomials haviug bounded coefficients bewhere g_1, g_2,…, g_n are linearly independent continuous functions defined on the interval [a, b], α_jβ_j, are extended real numbers satisfying α_j<+∞, β_j>?and α_j≤β_j.Assume that f is a continuousfunction defined on a compact set X[a, b]. In the paper, we first give the sufficient conditions forthe polynomial of best uniform approxmation to f from K being unique and strongly unique.Furthermore, we give two forms of necessary and sufficient conditions for the best approximationto be strongly unique.
Let the set of generalized polynomials haviug bounded coefficients bewhere g_1, g_2,…, g_n are linearly independent continuous functions defined on the interval [a, b], α_jβ_j, are extended real numbers satisfying α_j<+∞, β_j>?and α_j≤β_j.Assume that f is a continuousfunction defined on a compact set X[a, b]. In the paper, we first give the sufficient conditions forthe polynomial of best uniform approxmation to f from K being unique and strongly unique.Furthermore, we give two forms of necessary and sufficient conditions for the best approximationto be strongly unique.
