ESTIMATES OF THE REMAINDER IN TAYLOR'S THEOREM USING THE HENSTOCK-KURZWEIL INTEGRAL


    loading  Checking for direct PDF access through Ovid

Abstract

When a real-valued function of one variable is approximated by its nth degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue p-norms in cases where f(n) or f(n+1) are Henstock-Kurzweil integrable. When the only assumption is that f(n) is Henstock-Kurzweil integrable then a modified form of the nth degree Taylor polynomial is used. When the only assumption is that f(n)C0 then the remainder is estimated by applying the Alexiewicz norm to Schwartz distributions of order 1.

    loading  Loading Related Articles