In Pipkin's "A Course on Integral Equations", on page 24 problem 2, he asks us to find out whether or not iteration will converge uniformly for an integral equation of the second kind, i.e $u=f+Ku$ on the interval $[0,1]$, with kernel (b) $2\cdot|x-y|$.
Now the answer at the back of the book is that $||K||=2/3$ and thus the iteration does converge.
My problem is that I get that the norm of $K$ is 1.
Here's my calculations:
$$||K|| = 2\max_{x\in [0,1]} \int_{0}^{1} |x-y|dy$$
Now I get that this integral equals: $x^2-x+0.5$ in the domain of the unit interval it seems the absolute maximum is at x=1 which give 0.5, which means that the norm should be 1.
I can elaborate on my calculations, but it seems to me that I didn't get it wrong (I repeated my calculations three times...).
Am I wrong here?