Journal of Inequalities and Applications
Volume 1 (1997), Issue 4, Pages 335-343
Notes to G. Bennett’s problems
Bolyai Institute, József Attila University, Aradi Vértanúk tere 1, Szeged H-6720, Hungary
Received 16 November 1996
Copyright © 1997 L. Leindler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
G. Bennett showed, by elementary proof, that if then (1.1) holds, and the constant is best possible; and if then (1.2) is valid. The reversed inequalities have remained open problems. As a first step into the converse direction, what seems to be very intricate without additional assumptions, we prove the inverse inequalities under slight restrictions on the monotonicity of the parameters appearing in the problem.