EDB — 14D

[14D]Prerequisites:[2CS]↺↻,[118]↺↻.Let $C_b=C_b(I)$ be the space of continuous bounded functions $f:I:\to \mathbb{R})$. This is a Banach space (a complete normed space) with the norm $\Vert f{\Vert }_{\infty }=\underset{x}{sup}|f(x)|$.

Consider the map $F:[0,\infty )\times C_b\to C_b$ transforming $g=F(\epsilon ,f)$, as defined in the eqn. [(12.20)]↺↻.

Show that $F$ is continuous.