You could also use the special behaviour of the null filehandle <>. It reads file names from the @ARGV variable, which you can populate via the command line or manually. It opens each file specified and reads one line at a time. Here is a sample:

#!perl
use 5.012;

# Populate @ARGV unless files are specified on the command line
@ARGV = grep { -f } glob('/tmp/files/*') unless @ARGV;
while (<>) {
    chomp;
    if ( m/map/i ) {
        # The name of the current file is in the special variable $ARG
+V
        say "$_ in $ARGV";
    }
}
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See I/O Operators in perlop for more info.