INEQUALITIES OF THE COMPLETE ELLIPTIC INTEGRALS

Authors

  • FENG QI Department of M;:.thematics, Jiaozuo Institute of Technology, Jiaozuo City, Henan 454000, The People's Republic of China.
  • ZHENG HUANG Department of Mathematics, University of Science and Technology of China, Hefei City, Anhui 230026, The People's Republic of China.

DOI:

https://doi.org/10.5556/j.tkjm.29.1998.4242

Keywords:

Inequality, estimate complete elliptic integral, Tchebycheff's integral inequality

Abstract

In this article, using Tchebycheff's integral inequality, the authors establish some estimates and inequalities for three kinds of the complete elliptic integrals.

References

Bai-Ni Guo and Feng Qi, "lmprovemnet for the upper bound of a class of elliptic integral," Journal of Jiaozuo Mining Institute, 14(6)(1995), 125-128. (Chinese)

Ji-Chang Kuang, Applied Inequalities, 2nd edition, Hunan Education Press, Changsha, China, 1993. (Chinese)

Zi-Fen Lu, Gaodeng Shuxue Jiexi Daqun, Liaoning Press of Science and Technology, Shenyar1g, China, 1991. (Chinese)

D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970.

D.S. Mitrinovic, J.E. Pecaric and A. M. Fink, "Classical and New Inequalities in Analysis", Kluwer Acade而 c Publishers, Dordrecht/Boston/London, 1993.

Feng Qi, "Generalized weighted mean values with two parameters," Proc. Roy. Soc. London A, 454(1998), in the press.

Feng Qi, "On a two-parameter family of nonhomogeneous mean values," Tamkang Journal of Mathematics, 29(2)(1998), 83-91.

Feng Qi, Li-Hong Cui and Sen-Lin Xu, "Applications of Tehebycheff's integral inequality," Publ. Inst. Mat. Beograd. N. S. (1998), to appear.

Feng Qi and Bai-Ni Guo, "The estimation of inferior bound for an ellipse integral," Journal of Mathematics for Technology, 10(1)(1994), 87-90. (Chinese).

Feng Qi and Bai-Ni Guo, "Estimate for the upper bound of a complete elliptic integral", Mathematics in Practice and Theory, 26(3)(1996), 285-288. (Chinese)

Feng Qi and Sen-Lin Xu, "The function $(b^x - a^x)/x$: Inequalities and properties," Proc. Amer. Math. Soc. (1998), in the press.

T. M. Rassias R. H. Garstang and O. P. Lossers, "Bounds on an elliptic integral," Amer. Math. Monthly, 94(1987), 556-557.

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Published

1998-09-01

How to Cite

QI, F., & HUANG, Z. (1998). INEQUALITIES OF THE COMPLETE ELLIPTIC INTEGRALS. Tamkang Journal of Mathematics, 29(3), 165-169. https://doi.org/10.5556/j.tkjm.29.1998.4242

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