Just using glob should work, shouldn't cause an error:

foreach my $file ( glob('/tmp/files/*') )
{
        print "\n\nThe File is $file\n\n";
        open (MYFILE, "<$file") or die $! ;
        while (<MYFILE>) {
                chomp;
                if ( $_ =~ m/map/i )
                {
                        print "$_ in $file\n";
                }
        }
        close (MYFILE);
}
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