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 .

**[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 (Unpublished.)**[5]**R. E. Moore,*Interval Analysis*, Prentice-Hall, Englewood Cliffs, N. J., 1966.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 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 ,"*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