//the cart key stores information about cart
$cartKeySanitized = filter_var($_POST['cart_item_key'], FILTER_SANITIZE_STRING);
//the new qty you want for the product in cart
$cartQtySanitized = filter_var($_POST['cart_item_qty'], FILTER_SANITIZE_STRING);
//update the quantity
global $woocommerce;
ob_start();
$woocommerce->cart->set_quantity($cartKeySanitized,$cartQtySanitized);
ob_get_clean();
wp_footer(); ?>
