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An inequality with application to a difference equation

Published online by Cambridge University Press:  17 April 2009

Jong-Yi Chen  and
Yunshyong Chow
Jong-Yi Chen
Affiliation:
Department of Mathematical Education, National Hualien Teachers College, Hualien, Taiwan 970, e-mail: jongyi@mail.nhltc.edu.tw
Yunshyong Chow
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei, Taiwan 115, e-mail: chow@math.sinica.edu.tw
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In this paper we shall prove that for any 0 < d ≤ 2, holds for n ≥ 1.

As an application, we shall then show that the following recursively defined sequence

satisfies

The difference equation above originates from a heat conduction problem studied by Myshkis (J. Difference Equ. Appl. 3(1997), 89–91).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 519 - 528
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Chang, C.H., Chow, Y. and Wang, Z., ‘On the asymptotic behavior of heating times’, Anal. Appl. (Singap.) 1 (2003), 429–432.CrossRefGoogle Scholar
[2]Chen, Y.M., Chow, Y. and Hsieh, J., ‘On a heat conduction problem by Myshkis’, J. Differ. Equations Appl. 6 (2000), 309–318.CrossRefGoogle Scholar
[3]Hochstadt, H., The functions of mathematical physics (Wiley Interscience, New York, London, Sydney, 1971).Google Scholar
[4]Myshkis, A.D., ‘On a recurrently defined sequence’, J. Differ. Equations Appl. 3 (1997), 89–91.CrossRefGoogle Scholar