TY - JOUR
T1 - Nikolskii-type estimates for coconvex approximation of functions with one inflection point
AU - Dzyubenko, G. A.
AU - Leviatan, D.
AU - Shevchuk, I. A.
PY - 2010/6/21
Y1 - 2010/6/21
N2 - For each r ∈ N we prove the Nikolskii type pointwise estimate for coconvex approximation of functions f ∈ Wr, the subspace of all functions f ∈ C[-1, 1], possessing an absolutely continuous (r - 1)st derivative on (-1, 1) and satisfying f(r) ∈ L∞[-1, 1], that change their convexity once on [-1, 1].
AB - For each r ∈ N we prove the Nikolskii type pointwise estimate for coconvex approximation of functions f ∈ Wr, the subspace of all functions f ∈ C[-1, 1], possessing an absolutely continuous (r - 1)st derivative on (-1, 1) and satisfying f(r) ∈ L∞[-1, 1], that change their convexity once on [-1, 1].
KW - Coconvex polynomial approximation
KW - Pointwise estimates
UR - http://www.scopus.com/inward/record.url?scp=81855217428&partnerID=8YFLogxK
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AN - SCOPUS:81855217428
SN - 1889-3066
VL - 2
SP - 51
EP - 64
JO - Jaen Journal on Approximation
JF - Jaen Journal on Approximation
IS - 1
ER -