Inequalities between Arithmetic-Geometric, Gini, and Toader Means

We find the greatest values p(1), p(2) and least values q(1), q(2) such that the double inequalities Sp(1)(a, b) < M(a, b) < Sq(1)(a, b) and Sp(2)(a, B) < T(a, b) < Sq(2)(a, b) hold for all a, b > 0 with a not equal b and present some new bounds for the complete elliptic integrals. Here M(a, b), T(a, b), and S-p(a, b) are the arithmetic-geometric, Toader, and pth Gini means of two positive numbers a and b, respectively.