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Monotonicity of Certain Riemann Sums

Borwein, David and Borwein, Jonathan M. and Sims, Brailey (2015) Monotonicity of Certain Riemann Sums. (Submitted)

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    Abstract

    We consider conditions ensuring the monotonicity of right and left Rie- mann sums of a function f : [0,1] → R with respect to uniform partitions. Experimentation suggests that symmetrization may be important and leads us to results such as: if f is decreasing on [0,1] and its symmetrization, F (x) := 1 (f (x) + f (1 − x)) is concave then its right Riemann sums increase 2 monotonically with partition size. Applying our results to functions such as f (x) = 1/ (1 + x^2)also leads to a nice application of Descartes’ rule of signs.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 28 Mar 2016 12:25
    Last Modified: 28 Mar 2016 12:25
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1692

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