How to display update message only to admin

Create your own plugin with this code or put this in theme’s functions.php

add_action('init', 'remove_update_notification', 1)
function remove_update_notification() {
    if (!current_user_can('manage_network')) { // checks to see if current user can update plugins 
        add_action( 'init', create_function( '$a', "remove_action( 'init', 'wp_version_check' );" ), 2 );
        add_filter( 'pre_option_update_core', create_function( '$a', "return null;" ) );
    }
}