Try:
$mycategory = array(23, 33, 37);
if( is_category( $mycategory ) ) {
echo 'yes';
} else {
echo 'no';
}
is_category returns true if there are any matches.
You could try this:
...
$term = get_term_by( 'id', $child, $taxonomy_name);
if ( is_category( $term->term_id ) ) {
$mycategory[] = $term->term_id;
}