Taiwanese Journal of Mathematics

INVERSES OF SOME NEW INEQUALITIES SIMILAR TO HILBERT’S INEQUALITIES

Abstract

In the present paper we first establish inverse versions of some new inequalities similar to Hilbert’s inequality involving series of nonnegative terms. Then, the integral analogues of our main results are also given. Our Theorems provide new estimates on these types of inequalities.

Article information

Source
Taiwanese J. Math., Volume 10, Number 3 (2006), 699-712.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500403856

Digital Object Identifier
doi:10.11650/twjm/1500403856

Mathematical Reviews number (MathSciNet)
MR2206323

Zentralblatt MATH identifier
1105.26018

Subjects
Primary: 26D15: Inequalities for sums, series and integrals

Citation

Changjian, Zhao; Pecarić, Josip; Gangsong, Leng. INVERSES OF SOME NEW INEQUALITIES SIMILAR TO HILBERT’S INEQUALITIES. Taiwanese J. Math. 10 (2006), no. 3, 699--712. doi:10.11650/twjm/1500403856. https://projecteuclid.org/euclid.twjm/1500403856

References

• [1.] B. G. Pachpatte, On some new inequalities similar to Hilbert's inequality, J. Math. Anal. Appl., 226 (1998), 166-179.
• [2.] G. D. Handley, J. J. Koliha and J. E. Pečarić, New Hilbert-Pachpatte Type Integral Inequalities, J. Math. Anal. Appl., 257 (2001), 238-250.
• [3.] Gao Minzhe and Yang Bicheng, On the extended Hilbert's inequality, Proc. Amer. Math. Soc., 126 (1998), 751-759.
• [4.] Kuang Jichang, On new extensions of Hilbert's integral inequality, J. Math. Anal. Appl., 235 (1999), 608-614.
• [5.] Yang Bicheng, On new generalizations of Hilbert't inequality, J. Math. Anal. Appl., 248 (2000), 29-40.
• [6.] Zhao Changjian, On Inverses of disperse and continuous Pachpatte's inequalities, Acta Math. Sin., 46 (2003), 1111-1116.
• [7.] Zhao chang-jian, Generalizations on two new Hilbert type inequalities, J. Math., 20 (2000), 413-416.
• [8.] Zhao Changjian and L. Debnath, Some New Inverse Type Hilbert Integral Inequalities, J. Math. Anal. Appl., 262 (2001), 411-418.
• [9.] G. D. Handley, J. J. Koliha and J. E. Pečarić, A Hilbert type inequality, Tamkang J. Math., 31 (2000), 311-315.
• [10.] G. H. Hardy, J. E. Littlewood and P$\acute{o}$lya, Inequalities, Cambridge Univ. Press, Cambridge, U.K., 1934.
• [11.] E. F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, Berlin-G$\ddot{\rm o}$ttingen, Heidelberg, 1961.