Approximating real functions which possess nth derivatives of bounded variation and applications
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Dragomir, Sever S (2008) Approximating real functions which possess nth derivatives of bounded variation and applications. Computers and Mathematics with Applications, 56 (9). pp. 2268-2278. ISSN 0898-1221
Abstract
The main aim of this paper is to provide an approximation for the function f which possesses continuous derivatives up to the order n − 1 (n ≥ 1) and has the nth derivative of bounded variation, in terms of the chord that connects its end points A = (a, f (a)) and B = (b, f (b)) and some more terms which depend on the values of the k derivatives of the function taken at the end points a and b, where k is between 1 and n. Natural applications for some elementary functions such as the exponential and the logarithmic functions are given as well.
| Item type | Article |
| URI | https://vuir.vu.edu.au/id/eprint/3640 |
| Official URL | http://www.sciencedirect.com/science/journal/08981... |
| Subjects | Historical > Faculty/School/Research Centre/Department > School of Engineering and Science Historical > FOR Classification > 0101 Pure Mathematics Historical > SEO Classification > 970101 Expanding Knowledge in the Mathematical Sciences |
| Keywords | ResPubID15199. Taylor’s expansion, approximation, functions of bounded variation, analytic inequalities error bounds |
| Citations in Scopus | 13 - View on Scopus |
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