A note on a conjecture of L. J. Mordell
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- by Michael A. Malcolm PDF
- Math. Comp. 25 (1971), 375-377 Request permission
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
- P. H. Diananda, On a cyclic sum, Proc. Glasgow Math. Assoc. 6 (1963), 11–13 (1963). MR 150084
- D. Ž. Djoković, Sur une inégalité, Proc. Glasgow Math. Assoc. 6 (1963), 1–10 (1963) (French). MR 150083 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. M. A. Malcolm & J. Katzman, RAT-Range Arithmetic Translator, 1969. (Unpublished.)
- Ramon E. Moore, Interval analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. MR 0231516
- L. J. Mordell, On the inequality $\sum ^{n}_{r=1} \,x_{r}/(x_{r+1}+x_{r+2})\geqq n/2$ and some others, Abh. Math. Sem. Univ. Hamburg 22 (1958), 229–241. MR 96915, DOI 10.1007/BF02941955
- L. J. Mordell, Note on the inequality $\sum ^{n}_{r=1}\,x_{r}/(x_{r+1}+x_{r+2})\geq n/2$, J. London Math. Soc. 37 (1962), 176–178. MR 138580, DOI 10.1112/jlms/s1-37.1.176
- Pedro Nowosad, Isoperimetric eigenvalue problems in algebras, Comm. Pure Appl. Math. 21 (1968), 401–465. MR 238087, DOI 10.1002/cpa.3160210502 R. A. Rankin, "An inequality," Math. Gaz., v. 42, 1958, pp. 39-40.
- H. S. Shapiro, Richard Bellman, D. J. Newman, W. E. Weissblum, H. R. Smith, and H. S. M. Coxeter, Advanced Problems and Solutions: Problems for Solution: 4603-4607, Amer. Math. Monthly 61 (1954), no. 8, 571–572. MR 1528827, DOI 10.2307/2307617
- A. Zulauf, On a conjecture of L. J. Mordell, Abh. Math. Sem. Univ. Hamburg 22 (1958), 240–241. MR 124261, DOI 10.2307/3610955
Additional Information
- © Copyright 1971 American Mathematical Society
- 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