Moduli of smoothness of vector valued functions of a real variable and applications |
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| Authors: | Tzanko D. Donchev Elza M. Farkhi |
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| Affiliation: | 1. Dept. of Mathematics , Higher Institute of Mining and Geology , Sofia, 1156, Bulgaria;2. Bulgarian Academy of Sciences , Institute of Mathematics , Acad. G. Bonchev str., b1.8, Sofia, 1113, Bulgaria |
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| Abstract: | Moduli of smoothness of Banach space valued functions of a real argument are defined and studied. The classical Whitney's theorem on the error of polynomial approximation [7] is extended to this case. Estimates for quadrature formulae and numerical treatment of abstract differential equations are presented. Applications to the numerical analysis of set-valued maps, differential inclusions and interval functions are made. |
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