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Approximating real functions which possess nth derivatives of bounded variation and applications

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

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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
Uncontrolled Keywords: ResPubID15199. Taylor’s expansion, approximation, functions of bounded variation, analytic inequalities error bounds
Subjects: Faculty/School/Research Centre/Department > School of Engineering and Science
FOR Classification > 0101 Pure Mathematics
SEO Classification > 970101 Expanding Knowledge in the Mathematical Sciences
Depositing User: VUIR
Date Deposited: 13 Oct 2011 01:01
Last Modified: 12 Mar 2013 03:40
URI: http://vuir.vu.edu.au/id/eprint/3640
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Citations in Scopus: 2 - View on Scopus

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