menu-parent-item class filter

add_filter('wp_nav_menu_objects', 'add_menu_parent_class');

function add_menu_parent_class($items) {

    foreach ($items as &$item) {
        if (hasSub($item->ID, &$items)) {
            $item->classes[] = 'menu-parent-item'; // all elements of field "classes" of a menu item get join together and render to class attribute of <li> element in HTML
        }
    }
    return $items;
}

function hasSub($menu_item_id, &$items) {
        foreach ($items as $item) {
            if ($item->menu_item_parent && $item->menu_item_parent==$menu_item_id) {
                return true;
            }
        }
        return false;
};