Abstract :
We prove that the inequality
n 2 n n b
xkyk F yk a q xk2yk ). / /k ks1 ks1 ks1
holds for all natural numbers n and for all real numbers xkand yk ks1, . . . , n.
with
0-x1Fx2r2F ??? Fxnrn and 0-ynFyny1F ??? Fy1,
if and only if
a G3r4 and b G1ya .
Inequality ). with a s3r4 and b s1r4 refines results given by Liu Zheng J.
Math. Anal. Appl. 218 1998., 13]21.and the author J. Math. Anal. Appl. 168
1992., 596]604..
