How can I prove?.

Prove that if $[(b-a)|\lambda|sup_{t,s \in [a,b]}|\kappa (t,s)|]<1$, then a integral linear equation of Fredholm has a unique solution in $C[a,b]$.

We know by definition that; in a integral equation of fredholm $K(t,s,u)=\lambda \kappa(t,s)u, \lambda \in \mathbb{R}$, we obtain the integral linear equation of fredholm $\psi (t)= \lambda \int _{a} ^b \kappa (t,s) \psi(s) ds + \varphi(t), t\in [a,b]$.

  • $\begingroup$ What have you tried? What are your thoughts? $\endgroup$ – DisintegratingByParts Oct 11 '18 at 23:27

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.