CRISTINEL MORTICI 1, HU YUE 2 1. Valahia University of Târgovişte, Department of Mathematics,
Bd. Unirii 18, 130082 Târgovişte, ROMANIA, e-mail: cmortici@valahia.ro
2. College of Mathematics and Informatics, Henan Polytechnic University,
Jaozuo City, Henan 454000, China, e-mail: huu3y2@163.com
The aim of this note is to give an improvement of Carleman’s
inequality. The proof is elementary and our new inequality refines results stated by Bicheng and Debnath [Some inequlities involving the constant e and an application to Carleman’s inequlity. J. Math. Anal. Appl. 223 (1998) 347–353], Xie and Zhong [A best approximation for constant e and an improvement to Hardy’s inequality J. Math. Anal. Appl. 252 (2000) 994–998.], Ping and Guozheng [A Strengthened Carleman’s inequality. J. Math. Anal. Appl. 240 (1999) 290–293] and Yang [On Carleman’s inequality J. Math. Anal. Appl. 253 (2001) 691–694].
