Show that defined by (24.7) gives rise to a complete normed linear space. Suppose g(t) is non-negative and bounded on each finite subinterval of [0,∞). Suppose there exist constants A and B such...

Show that

defined by (24.7) gives rise to a complete normed linear space.

Suppose g(t) is non-negative and bounded on each finite subinterval of [0,∞). Suppose there exist constants A and B such that

for each

Prove that

This result is known as Gronwall’s lemma.

use (24.21) to substitute for g(r), and iterate.