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On some switching inequalities of Brenner and Alzer

Published online by Cambridge University Press:  17 February 2009

C. E. M. Pearce  and
J. Pečarić
C. E. M. Pearce
Affiliation:
School of Applied Mathematics, The University of Adelaide, Adelaide SA 5005, Australia; e-mail: [email protected].
J. Pečarić
Affiliation:
Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 1000 Zagreb, Croatia; e-mail: [email protected].
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Abstract

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We consider some general switching inequalities of Brenner and Alzer. It is shown that Brenner's Theorem B below does not hold in general without further conditions. A simple proof is given of Alzer's Corollary D.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 2 , October 2003 , pp. 285 - 288
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Alzer, H., “On an inequality of J. L. Brenner”, J. Math. Anal. Applic. 183 (1994), 547–550.Google Scholar
[2]Brenner, J. L., “Some inequalities from switching theory”, J. Combin. Theory 7 (1969), 197–205.Google Scholar
[3]Brenner, J. L., “Analytical inequalities with applications to special functions”, J. Math. Anal. Appl. 106 (1985), 427–442.Google Scholar
[4]Lehman, A., “Problem 60-5, A resistor network inequality”, SIAM Rev. 4 (1962), 150–155; 2 (1960), 152–153.Google Scholar
[5]Lehman, A., “A solution of the Shannon switching game”, SIAM J. 12 (1964), 687–725.Google Scholar
[6]Turner, J. C. and Conway, V., “Problem 68-1, A network inequality”, SIAM Rev. 10 (1968), 107–108.Google Scholar