- 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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