Once again from the the WP developer holy bible … ;-)
Disable Plugin and Theme update notice
IMHO, I think this is the right way
This will block users being able to use the plugin and theme installation/update functionality from the WordPress admin area. Setting this constant also disables the Plugin and Theme editor (i.e. you don’t need to set DISALLOW_FILE_MODS and DISALLOW_FILE_EDIT, as on it’s own DISALLOW_FILE_MODS will have the same effect).
define('DISALLOW_FILE_MODS',true);
Disable Core update notice
It’s true that to keep it secure, it would better to update the core as soon as a new stable release or sub-release is out; but it’s true that some clients (i call them ‘smanettoni’) keep all days trying to broke things so in that cases I prefer to lock down the site to prevent accidental and unwanted issues.
There are thousands of pages if you google the subject but what i prefer (as a developer) is the solution based on WP filters and not on plugins taken from wpmu.org ; ok so.. here it is:
Simply add this to your functions.php file and click save and the notices will disappear.
add_filter( 'pre_site_transient_update_core', create_function( '$a', "return null;" ) );
Thats the way i like it.. ah ah
And what about you ???