The shooting method applied to a cyclic inequality

Author:
B. A. Troesch

Journal:
Math. Comp. **34** (1980), 175-184

MSC:
Primary 10E20

DOI:
https://doi.org/10.1090/S0025-5718-1980-0551296-2

MathSciNet review:
551296

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Abstract | References | Similar Articles | Additional Information

Abstract: It is known that the cyclic sum

**[1]**D. E. Daykin,*Inequalities for functions of a cyclic nature*, J. London Math. Soc. (2)**3**(1971), 453–462. MR**0284394**, https://doi.org/10.1112/jlms/s2-3.3.453**[2]**P. H. Diananda,*On a cyclic sum*, Proc. Glasgow Math. Assoc.**6**(1963), 11–13 (1963). MR**0150084****[3]**P. H. Diananda,*A cyclic inequality and an extension of it. II*, Proc. Edinburgh Math. Soc. (2)**13**(1962/1963), 143–152. MR**0148831**, https://doi.org/10.1017/S0013091500014711**[4]**D. Ž. Djoković,*Sur une inégalité*, Proc. Glasgow Math. Assoc.**6**(1963), 1–10 (1963) (French). MR**0150083****[5]**D. S. Mitrinović,*Analytic inequalities*, Springer-Verlag, New York-Berlin, 1970. In cooperation with P. M. Vasić. Die Grundlehren der mathematischen Wissenschaften, Band 165. MR**0274686****[6]**Pedro Nowosad,*Isoperimetric eigenvalue problems in algebras*, Comm. Pure Appl. Math.**21**(1968), 401–465. MR**0238087**, https://doi.org/10.1002/cpa.3160210502**[7]**R. A. RANKIN, "An inequality,"*Math. Gaz.*, v. 42, 1958, pp. 39-40.**[8]**J. L. Searcy and B. A. Troesch,*A cyclic inequality and a related eigenvalue problem*, Pacific J. Math.**81**(1979), no. 1, 217–226. MR**543745****[9]**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**, https://doi.org/10.2307/2307617

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1980-0551296-2

Keywords:
Cyclic inequality,
shooting method,
minimization

Article copyright:
© Copyright 1980
American Mathematical Society