How to put an array in is_category

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;
}