No, even if $$$p, q, r, s \ge 0$$$ you can't say for sure, counter-example: $$$a_1 = 5, a_2 = 5, a_3 = 3, a_4 = 5$$$ & $$$b_1 = 4, b_2 = 4, b_3 = 5, b_4 = 4$$$ then with $$$p = 1, q = 1, r = 2, s = 1$$$ the inequality does not hold.