Abstract
The topologies induced by two families of seminorms on a vector space of functions $g:{R^ + } \times {R^ + } \times {E^n} \to {E^n}$ are compared. It is found that the continuous dependence of solutions of the Volterra equation $x(t) = f(t) + \int {_0^tg(t,s,x(s))ds}$ does not hold for the weaker topology. This result corrects an error in the book of Miller, Benjamin, Menlo Park, Calif., 1971.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.