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 cyclic nature,"*J. London Math. Soc.*(2), v. 3, 1971, pp. 453-462. MR**0284394 (44:1622a)****[2]**P. H. DIANANDA, "On a cyclic sum,"*Proc. Glasgow Math. Assoc.*, v. 6, 1963, pp. 11-13. MR**0150084 (27:87)****[3]**P. H. DIANANDA, "A cyclic inequality and an extension of it. II,"*Proc. Edinburgh Math. Soc.*(2), v. 13, 1962/1963, pp. 143-152. MR**0148831 (26:6335)****[4]**D. Ž. DJOKOVIĆ, "Sur une inégalité,"*Proc. Glasgow Math. Assoc.*, v. 6, 1963, pp. 1-10. MR**0150083 (27:86)****[5]**D. S. MITRINOVIĆ,*Analytic Inequalities*, Springer-Verlag, New York, 1970, p. 132 ff. MR**0274686 (43:448)****[6]**P. NOWOSAD, "Isoperimetric eigenvalue problems in algebra,"*Comm. Pure Appl. Math.*, v. 21, 1968, pp. 401-465. MR**0238087 (38:6363)****[7]**R. A. RANKIN, "An inequality,"*Math. Gaz.*, v. 42, 1958, pp. 39-40.**[8]**J. L. SEARCY & B. A. TROESCH, "A cyclic inequality and a related eigenvalue problem,"*Pacific J. Math.*, v. 81, 1979, pp. 217-226. MR**543745 (80f:15019)****[9]**H. S. SHARIRO, "Problem 4603,"*Amer. Math. Monthly*, v. 61, 1954, p. 571. MR**1528827**

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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