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Journal of Function Spaces
Volume 2018 (2018), Article ID 9569380, 8 pages
https://doi.org/10.1155/2018/9569380
Research Article

On a New Extension of Mulholland’s Inequality in the Whole Plane

1Department of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 51003, China
2Guangxi Colleges and Universities Key Laboratory of Intelligent Processing of Computer Image and Graphics, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China
3Department of Computer Science, Guangdong University of Education, Guangzhou, Guangdong 51003, China

Correspondence should be addressed to Yanru Zhong

Received 4 November 2017; Accepted 12 December 2017; Published 1 February 2018

Academic Editor: Pasquale Vetro

Copyright © 2018 Bicheng Yang et al. 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.

Linked References

  1. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, 1934. View at MathSciNet
  2. D. S. Mitrinović, J. E. Pečarić, and A. M. Fink, Inequalities involving functions and their integrals and derivatives, vol. 53 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  3. B. Yang, “A new Hilbert's type integral inequality,” Soochow Journal of Mathematics, vol. 33, no. 4, pp. 849–859, 2007. View at Google Scholar · View at MathSciNet
  4. Y. Hong, “All-sided generalization about Hardy-Hilbert integral inequalities,” Acta Mathematica Sinica, vol. 44, no. 4, pp. 619–626, 2001. View at Google Scholar · View at MathSciNet
  5. L. E. Azar, “On some extensions of Hardy-Hilbert's inequality and applications,” Journal of Inequalities and Applications, vol. 2008, Article ID 546829, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. Krnić and J. Pecarić, “General Hilbert's and Hardy's inequalities,” Mathematical Inequalities & Applications, vol. 8, no. 1, pp. 29–51, 2005. View at Google Scholar · View at MathSciNet
  7. I. Perić and P. Vuković, “Multiple Hilbert's type inequalities with a homogeneous kernel,” Banach Journal of Mathematical Analysis, vol. 5, no. 2, pp. 33–43, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  8. B. He and Q. Wang, “A multiple Hilbert-type discrete inequality with a new kernel and best possible constant factor,” Journal of Mathematical Analysis and Applications, vol. 431, no. 2, pp. 889–902, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. V. Adiyasuren, T. Batbold, and M. Krnić, “Multiple Hilbert-type inequalities involving some differential operators,” Banach Journal of Mathematical Analysis, vol. 10, no. 2, pp. 320–337, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  10. Y. Li and B. He, “On inequalities of Hilbert's type,” Bulletin of the Australian Mathematical Society, vol. 76, no. 1, pp. 1–13, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. W. Zhong, “A Hilbert-type linear operator with the norm and its applications,” Journal of Inequalities and Applications, vol. 2009, Article ID 494257, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. Q. Huang, “On a Multiple hilbert's inequality with parameters,” Journal of Inequalities and Applications, vol. 2010, Article ID 309319, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. M. Krnić and P. Vuković, “On a multidimensional version of the Hilbert type inequality,” Analysis Mathematica, vol. 38, no. 4, pp. 291–303, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. Q. Huang, “A new extension of a Hardy-Hilbert-type inequality,” Journal of Inequalities and Applications, vol. 2015, article 397, 12 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Q. Huang and B. Yang, “A more accurate half-discrete hilbert inequality with a nonhomogeneous kernel,” journal of function spaces and applications, vol. 2013, Article ID 628250, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. B. Yang and Q. Chen, “A new extension of Hardy-Hilbert's inequality in the whole plane,” Journal of Function Spaces, vol. 2016, Article ID 9197476, pp. 1–8, 2016. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Xin, B. Yang, and Q. Chen, “A discrete Hilbert-type inequality in the whole plane,” Journal of Inequalities and Applications, vol. 2016, no. 1, article no. 133, 2016. View at Publisher · View at Google Scholar · View at Scopus
  18. J. Kuang, Applied inequalities, Shangdong Science Technic Press, Jinan, China, 2010.