Affiliation:
1. CONICET, Facultad de Ciencias Exactas Físico‐Químicas y Naturales Universidad Nacional de Río Cuarto Río Cuarto Argentina
2. Facultad de Ingeniería Universidad Nacional de La Pampa General Pico Argentina
Abstract
AbstractIn this paper, we obtain inequalities involving the Taylor polynomial and weak derivatives of a function in an Orlicz–Sobolev type space. Moreover, we show that any such function can be expanded in a finite Taylor series almost everywhere. As a consequence, we prove that the coefficients of any extended best polynomial ‐approximation of a function on a ball almost everywhere converge to the weak derivatives of such a function when the radius tends to 0. Lastly, we get a mean convergence result of such coefficients.
Funder
Agencia Nacional de Promoción Científica y Tecnológica
Consejo Nacional de Investigaciones Científicas y Técnicas
Universidad Nacional de Río Cuarto
Cited by
1 articles.
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