Polynomial approximation on convex polytopes in $/mathbf{R}^d$ is considered in uniform and $L^p$-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the $L^p$-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate $K$-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.
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स्वरूप PDF ● पेज 112 ● ISBN 9781470418946 ● प्रकाशक American Mathematical Society ● डाउनलोड करने योग्य 3 बार ● मुद्रा EUR ● आईडी 8056962 ● कॉपी सुरक्षा Adobe DRM
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