On a new Hardy-Mulholland-type inequality and its more accurate form
© Li et al. 2016
Received: 7 December 2015
Accepted: 8 February 2016
Published: 19 February 2016
Using weight coefficients and applying the well-known Hermite-Hadamard inequality, a new Hardy-Mulholand-type inequality with a best possible constant factor is given. Furthermore, we also consider the more accurate equivalent forms, the operator expressions and some particular inequalities. The lemmas and theorems provide an extensive account of this type of inequalities.
In this paper, using the way of weight coefficients and applying Hermite-Hadamard’s inequality, a Hardy-Mulholland-type inequality with a best possible constant factor similar to (6) is proved, which is an extension of (3). Furthermore, the more accurate Hardy-Mulholland-type inequality is built by introducing a few parameters. We also consider the equivalent forms, the operator expressions and some particular inequalities.
2 Some lemmas and an example
3 Main results
This work is supported by Hunan Province Natural Science Foundation (No. 2015JJ4041), and the National Natural Science Foundation of China (No. 61370186). Thanks for their help.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
- Hardy, GH, Littlewood, JE, Pólya, G: Inequalities. Cambridge University Press, Cambridge (1934) Google Scholar
- Yang, BC: Discrete Hilbert-Type Inequalities. Bentham Science Publishers, Sharjah (2011) Google Scholar
- Mulholland, HP: Some theorems on Dirichlet series with positive coefficients and related integrals. Proc. Lond. Math. Soc. 29(2), 281-292 (1929) View ArticleMathSciNetMATHGoogle Scholar
- Mitrinović, DS, Pečarić, JE, Fink, AM: Inequalities Involving Functions and Their Integrals and Derivatives. Kluwer Academic, Boston (1991) View ArticleMATHGoogle Scholar
- Yang, BC: Hilbert-Type Integral Inequalities. Bentham Science Publishers, Sharjah (2009) Google Scholar
- Yang, BC: On Hilbert’s integral inequality. J. Math. Anal. Appl. 220, 778-785 (1998) View ArticleMathSciNetMATHGoogle Scholar
- Yang, BC: An extension of Mulholland’s inequality. Jordan J. Math. Stat. 3(3), 151-157 (2010) MATHGoogle Scholar
- Chen, Q, Yang, BC: A survey on the study of Hilbert-type inequalities. J. Inequal. Appl. 2015, 302 (2015) View ArticleGoogle Scholar
- Yang, BC: The Norm of Operator and Hilbert-Type Inequalities. Science Press, Beijing (2009) (China) Google Scholar
- Yang, BC: An extension of a Hardy-Hilbert-type inequality. J. Guangdong Univ. Educ. 35(3), 1-7 (2015) Google Scholar
- Wang, DX, Guo, DR: Introduction to Spectral Functions. Science Press, Beijing (1979) (China) Google Scholar
- Huang, QL, Yang, BC: A more accurate Hardy-Hilbert-type inequality. J. Guangdong Univ. Educ. 35(5), 27-35 (2015) Google Scholar
- Yang, BC, Chen, Q: On a Hardy-Hilbert-type inequality with parameters. J. Inequal. Appl. 2015, 339 (2015) View ArticleGoogle Scholar
- Wang, AZ, Huang, QL, Yang, BC: A strengthened Mulholland-type inequality with parameters. J. Inequal. Appl. 2015, 329 (2015) View ArticleMathSciNetGoogle Scholar
- Kuang, JC: Applied Inequalities. Shangdong Science Technic Press, Jinan (2004) Google Scholar