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A note on the order of polynomial-like iterative equations

Draga S.

Commentationes Mathematicae

2016

Vol 56, No. 2

243--249

We show that, under reasonable assumptions, two negative roots can be eliminated from the characteristic equation of a polynomial-like iterative equation. This result gives a new case where we may lower the order of such an equation.

On orthogonally additive functions with orthogonally additive second iterate

Baron K.

Commentationes Mathematicae

2013

Vol. 53, No. 2

301--304

Let E be a real inner product space of dimension at least 2. If f maps E onto E and both f and f∘f are orthogonally additive, then f is additive.

An invariance of the geometric mean with respect to Lagrangian conditionally homogeneous mean-type mappings

Głazowska D.

Demonstratio Mathematica

2007

Vol. 40, nr 2

289-302

We determine all the Lagrangian conditionally homogeneous mean-type mappings for which the geometric mean is invariant.