if ($entry3 !~ /${user_input}_ABC_\S*\.pdf/) { ... }

##</code><code>##

use Path::Iterator::Rule;

...

my $rule = Path::Iterator::Rule->new;

$rule->file->not_name( qr/${user_input}_ABC_\S*\.pdf/ );
my $next = $rule->iter( $doc_dir );

while (defined( my $file = $next->() )) { ... }