HiMHFmembers,

I have a problem where I can reduce it to an integral equation of the form

$\displaystyle x(t)=(Tx)(t)$ for $\displaystyle t\in[a,b]$,

where

$\displaystyle (Tx)(t):=\int_{a}^{t}\int_{u}^{b}\frac{(t-u)^{k-1}}{(k-1)!}\frac{(v-u)^{n-k-1}}{(n-k-1)!}x(v)\mathrm{d}v\mathrm{d}u$ for $\displaystyle t\in[a,b]$.

Here, $\displaystyle 0\leq k\leq n-1$.

I tried to show that

$\displaystyle \lim_{k\to\infty}|(T^{k}x)(t)|=0$ for $\displaystyle t\in[a,b]$.

But I couldnotfind it.

Although I could prove what I need, I wonder to see if this is possible.

Thanks.

bkarpuz