Symmetry and the monotonicity of certain Riemann sums

Title: Symmetry and the monotonicity of certain Riemann sums
Creator: Borwein, David; Borwein, Jonathan M.; Sims, Brailey
Relation: JBCC: Jonathan M. Borwein Commemorative Conference. Springer Proceedings in Mathematics & Statistics (Callaghan, Australia 25-29 September, 2017) p. 7-20
Publisher Link: http://dx.doi.org/10.1007/978-3-030-36568-4_2
Publisher: Springer
Resource Type: conference paper
Date: 2020
Description: We consider conditions ensuring the monotonicity of right and left Riemann 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):=12(f(x)+f(1−x)) , is concave then its right Riemann sums increase monotonically with partition size. Applying our results to functions such as f(x)=1/(1+x2) also leads to a nice application of Descartes’ rule of signs.
Subject: descartes; monotonicity; Riemann sums; symmetrization
Identifier: http://hdl.handle.net/1959.13/1445736
Identifier: uon:42654
Identifier: ISBN:9783030365677
Language: eng
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