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A note on a conjecture of L. J. Mordell


Author: Michael A. Malcolm
Journal: Math. Comp. 25 (1971), 375-377
MSC: Primary 10.05; Secondary 68.00
DOI: https://doi.org/10.1090/S0025-5718-1971-0284395-8
MathSciNet review: 0284395
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Abstract | References | Similar Articles | Additional Information

Abstract: A computer proof is described for a previously unsolved problem concerning the inequality $ \sum\nolimits_{i = 1}^n {{x_i}/({x_{i + 1}} + {x_{i + 2}}) \geqq n/2} $.


References [Enhancements On Off] (What's this?)

  • [1] P. H. Diananda, "On a cyclic sum," Proc. Glasgow Math. Assoc., v. 6, 1963, pp. 11-13. MR 27 #87. MR 0150084 (27:87)
  • [2] D. Z. Djokovic, "Sur une inégalité," Proc. Glasgow Math. Assoc., v. 6, 1963, pp. 1-10. MR 27 #86. MR 0150083 (27:86)
  • [3] J. Alan George, FMIN1-Local Minimum of a Real Scalar Function of Several Variables Using a Gradient Search Method, Computer Science Department Program Library, Stanford University, Stanford, Calif., 1968.
  • [4] M. A. Malcolm & J. Katzman, RAT-Range Arithmetic Translator, 1969. (Unpublished.)
  • [5] R. E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1966. MR 37 #7069. MR 0231516 (37:7069)
  • [6] L. J. Mordell, "On the inequality $ \sum\nolimits_{{r = 1}^n} {x_r}/({x_{r + 1}} + {x_{r + 2}}) \geqq n/2 $ and some others," Abh. Math. Sem. Univ. Hamburg, v. 22, 1958, pp. 221-240. MR 0096915 (20:3397)
  • [7] L. J. Mordell, "Note on the inequality $ \sum\nolimits_{{r = 1}^n} {x_r}/({x_{r + 1}} + {x_{r + 2}}) \geqq n/2 $," J. London Math. Soc., v. 37, 1962, pp. 176-178. MR 25 #2023. MR 0138580 (25:2023)
  • [8] Pedro Nowosad, "Isoperimetric eigenvalue problems in algebras," Comm. Pure Appl. Math., v. 21, 1968, pp. 401-465. MR 38 #6363. MR 0238087 (38:6363)
  • [9] R. A. Rankin, "An inequality," Math. Gaz., v. 42, 1958, pp. 39-40.
  • [10] H. S. Shapiro, "Problem 4603," Amer. Math. Monthly, v. 61, 1954, p. 571. MR 1528827
  • [11] Von A. Zulauf, "Note on a conjecture of L. J. Mordell," Abh. Math. Sem. Univ. Hamburg, v. 22, 1968, pp. 240-241. MR 0124261 (23:A1575)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0284395-8
Keywords: Cyclic sum, interval arithmetic
Article copyright: © Copyright 1971 American Mathematical Society

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