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Computable Linear Orders and Limitwise Monotonic Functions

open access: yesJournal of Mathematical Sciences, 2021
In this paper, we describe the technique of extremely monotonic functions in the theory of computable linear orders. The basic definitions of extremely monotonic functions and their generalizations are given, and a number of their basic properties and ...
A N Frolov, M V Zubkov, Frolov A N
exaly   +1 more source

Pointwise Monotonic Functions and Generalized Subadditivity

open access: yesReal Analysis Exchange, 2013
A real function \(f\) defined in an open interval \(I\) is called increasing at a point \(x_0\in I\) if \[ \limsup_{x\to x_0-} f(x) \leq f(x_0 ) \leq \liminf_{x\to x_0+} f(x) \] and \(f\) is called pointwise increasing in \(I\) if it is increasing at every point of \(I\). Analogously, we define a pointwise decreasing function (see [\textit{J. Matkowski}
exaly   +3 more sources

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