Abstract
The objective of this research is to show the monotonicity properties of the trapezoid sum sequence in general of nonconvex or nonconcave real valued continuous functions on interval corresponding to partitions of obtained by dividing into equal length subintervals. The decreasing monotony of the trapezoid sum generically does not happen in class of nonconcave functions. The same thing happens when restricted to the monotone nonconcave functions, namely in class of nonconcave increasing or nonconcave decreasing functions. Furthermore, in class of nonconvex functions, the trapezoid sum sequence generically does not increasing, as well as in class of increasing nonconvex or decreasing nonconvex functions.
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