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Involutions of real intervals

Gaetano Zampieri (2014)

Annales Polonici Mathematici

This paper shows a simple construction of continuous involutions of real intervals in terms of continuous even functions. We also study smooth involutions defined by symmetric equations. Finally, we review some applications, in particular a characterization of isochronous potentials by means of smooth involutions.

Iterated quasi-arithmetic mean-type mappings

Paweł Pasteczka (2016)

Colloquium Mathematicae

We work with a fixed N-tuple of quasi-arithmetic means M , . . . , M N generated by an N-tuple of continuous monotone functions f , . . . , f N : I (I an interval) satisfying certain regularity conditions. It is known [initially Gauss, later Gustin, Borwein, Toader, Lehmer, Schoenberg, Foster, Philips et al.] that the iterations of the mapping I N b ( M ( b ) , . . . , M N ( b ) ) tend pointwise to a mapping having values on the diagonal of I N . Each of [all equal] coordinates of the limit is a new mean, called the Gaussian product of the means M , . . . , M N taken on b. We effectively...

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