Approximating real functions which possess nth derivatives of bounded variation and applications
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 I and n. Natural applications for some elementary functions such as the exponential and the logarithmic functions are given as well. (C) 2008 Elsevier Ltd. All rights reserved.
approximation taylor's expansion functions of bounded variation analytic inequalities error bounds