TY - JOUR
T1 - Interpolatory pointwise estimates for polynomial approximation
AU - Gonska, H. H.
AU - Leviatan, D.
AU - Shevchuk, I. A.
AU - Wenz, H. J.
PY - 2000
Y1 - 2000
N2 - We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f ∈ C[0, 1], by polynomials. For the sake of completeness, as well as in order to strengthen some existing results, we discuss briefly the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory estimates are achievable by proving affirmative results and by providing the necessary counterexamples in all other cases.
AB - We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f ∈ C[0, 1], by polynomials. For the sake of completeness, as well as in order to strengthen some existing results, we discuss briefly the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory estimates are achievable by proving affirmative results and by providing the necessary counterexamples in all other cases.
KW - Approximation by polynomials
KW - Degree of approximation
KW - Interpolatory pointwise estimates
KW - Shape-preserving approximation
UR - http://www.scopus.com/inward/record.url?scp=0034354662&partnerID=8YFLogxK
U2 - 10.1007/s003650010008
DO - 10.1007/s003650010008
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AN - SCOPUS:0034354662
SN - 0176-4276
VL - 16
SP - 603
EP - 629
JO - Constructive Approximation
JF - Constructive Approximation
IS - 4
ER -