科研之友
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摘要
For alpha, beta is an element of (0, 1/2) we prove that the double inequality G(alpha a + (1 - alpha)b, alpha b + (1 - alpha)a) < P (a, b) < G (beta a + ( 1-beta)b, beta b+ (1-beta)a) holds for all a, b > 0 with a not equal b if and only if alpha <= (1-root 1-4/pi(2))/2 and beta >= (3 - root 3)/6. Here, G(a, b) and P(a, b) denote the geometric and Seiffert means of two positive numbers a and b, respectively.
