Just change your for loop :
for index in ${array_item[*]}
do
check_$index
done
Full script
#!/bin/bash
array_item=(item1 item2)
#function
check_item1 ()
{
echo "hello from item1"
}
check_item2 ()
{
echo "Hello from item2"
}
for index in ${array_item[*]}
do
check_$index
done
NB: In addition the following funky constructs are available:
${array_item[*]} # All of the items in the array
${!array_item[*]} # All of the indexes in the array
${#array_item[*]} # Number of items in the array
${#array_item[0]} # Length of item zero