$mystring =~ s/$mytest1/$myrep1/g;

#!/usr/bin/perl 
 
use strict; 
use warnings; 
 
my $mytest1 = "\\\\abc"; # escape backslash twice: Once for the definition and once for the regex. 
my $myrep1 = "@\\abc"; # escape backslash once for the regex. 
my $mystring = "some string containing \\abc \\abc a couple of times"; # escape backslash once for the definition. 
 
$mystring = ~s/$mytest1/$myrep1/g;  
 
print "$mystring\n";

some string containing @\abc @\abc a couple of times

#!/usr/bin/perl  
  
use strict;  
use warnings;  
  
my $mytest1 = '\abc'; # no escape necessary because of the single-quotes 
my $myrep1 = '@\abc'; # same as above 
my $mystring = '\abc \abc'; # no escapes because this is like input from a file  
  
$mystring =~ s/\Q$mytest1\E/$myrep1/g; # \Q escapes the necessary meta characters   
  
print $mystring;