Lithuanian Mathematical Journal

, Volume 55, Issue 3, pp 343–366 | Cite as

An extended product integral, a modified linear integral equation, and functions of bounded p-variation*

  • Šarūnas Dirmeikis
  • Rimas Norvaiša


A usual linear Henstock–Kurzweil integral equation with respect to a simple discontinuous function may not have a solution. We propose to replace the value of the integral at the right endpoint of the integration domain by the left limit of its other values. We prove that the modified linear Henstock–Kurzweil integral equation with respect to a function h of bounded p-variation has a unique solution given by an extended Henstock–Kurzweil product integral of h over a right open interval.


Henstock–Kurzweil integral product integral p-variation linear integral equation 


26A42 26A45 45A05 


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsVilnius UniversityVilniusLithuania
  2. 2.Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania

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