Zlib problem in Ubuntu 14.04 – Backups won't work

Try creating a file wp-content/mu-plugins/gzopen.php (you will need to create the directory wp-content/mu-plugins if it does not already exist), with these contents:

if (!function_exists('gzopen') && function_exists('gzopen64')) {
function gzopen($filename , $mode = 'r', $use_include_path = 0 )
{
return gzopen64($filename , $mode, $use_include_path);
}
}

That ought to provide you with a temporary workaround.

Best wishes,
David