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CRITERIA FOR THE SEQUENCE OF DIFFERENCES OF A BOUNDED SEQUENCE TO BE NULL

Published online by Cambridge University Press:  17 September 2012

DAVID BORWEIN*
Affiliation:
Department of Mathematics, Western University, London ON, Canada N6A 5B7 (email: [email protected])
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Abstract

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Conditions are established for the sequence of differences $\{a_n-a_{n-1}\}$ of a bounded sequence $\{a_n\}$ of complex terms to converge to zero when a certain linear nonhomogeneous difference expression of the form $k_0 a_n+k_1a_{n-1}+\cdots +k_na_0$tends to zero as$n\to \infty .$

Type
Research Article
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

References

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