Approximating real functions which possess n n th derivatives of bounded variation and applications
The main aim of this paper is to provide an approximation for the function f f which possesses continuous derivatives up to the order n?1(n?1) n ? 1 ( n ? 1 ) and has the n n th derivative of bounded variation, in terms ofthe chord that connects its end points A=(a,f(a)) A = ( a , f ( a ) ) and B=(b,f(b)) B = ( b , f ( b ) ) and some more terms which depend on the values of the k k derivatives of the function taken at the end points a a and b b , where k k is between 1 and n n . Natural applications for some elementary functions such as the exponential and the logarithmic functions are given as well.
approximation taylors expansion functions of bounded variation analytic inequalities error bounds