All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 6 of 6

Showing per page

Equations containing locally Henstock-Kurzweil integrable functions

Seppo Heikkilä, Guoju Ye (2012)

Applications of Mathematics

A fixed point theorem in ordered spaces and a recently proved monotone convergence theorem are applied to derive existence and comparison results for solutions of a functional integral equation of Volterra type and a functional impulsive Cauchy problem in an ordered Banach space. A novel feature is that equations contain locally Henstock-Kurzweil integrable functions.

Estimates of the remainder in Taylor’s theorem using the Henstock-Kurzweil integral

Erik Talvila (2005)

Czechoslovak Mathematical Journal

When a real-valued function of one variable is approximated by its n th 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 n th degree Taylor polynomial is used. When the only assumption is that f ( n ) ∈ C 0 then the remainder is estimated by applying the Alexiewicz norm to Schwartz distributions of order 1.

Currently displaying 1 – 6 of 6

Page 1