Open Access
March 2007 Orthosymmetrical monotone functions
B. De Baets, K. C. Maes
Bull. Belg. Math. Soc. Simon Stevin 14(1): 99-116 (March 2007). DOI: 10.36045/bbms/1172852247


A straightforward generalization of the classical inverse of a real function based on reflections leads to several insuperable difficulties. We introduce a new type of inverse w.r.t. monotone bijections $\phi$ that is determined by the direction of the base vectors of the real Euclidean plane. Inverting a monotone function in the real plane does not necessarily result in a function. Given an increasing real function $f$, Schweizer and Sklar geometrically construct a set of inverse functions. We will largely extend their construction to our new concept of $\phi$-inverses, also incorporating decreasing functions $f$. Furthermore, the geometrical and algebraical aspects of our approach are elaborated comprehensively. Special attention goes to the symmetry of a monotone function $f$ w.r.t. some monotone bijection $\phi$.


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B. De Baets. K. C. Maes. "Orthosymmetrical monotone functions." Bull. Belg. Math. Soc. Simon Stevin 14 (1) 99 - 116, March 2007.


Published: March 2007
First available in Project Euclid: 2 March 2007

zbMATH: 1142.26007
MathSciNet: MR2327329
Digital Object Identifier: 10.36045/bbms/1172852247

Keywords: inverse , Real function , symmetry

Rights: Copyright © 2007 The Belgian Mathematical Society

Vol.14 • No. 1 • March 2007
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