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 \(\| f\| _∞=\sup _ x |f(x)|\).

Consider the map \(F:[0,∞)× C_ b→ C_ b\) transforming \(g=F(\varepsilon ,f)\), as defined in the eqn. [(12.20)]↺↻.

Show that \(F\) is continuous.