caa a22 4500 605508984 CHVBK 20210128100639.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00010-014-0297-z doi (NATIONALLICENCE)springer-10.1007/s00010-014-0297-z Chudziak Jacek Faculty of Mathematics and Natural Sciences, University of Rzeszów, Prof. St. Pigonia 1, 35-310, Rzeszów, Poland aut On functional equation stemming from utility theory and psychophysics [Elektronische Daten] [Jacek Chudziak] We deal with the functional equations $$f(\sigma(y)x + (1 - \sigma(y))y) = \tau(y)f(x) + (1 - \tau(y))f(y)$$ f ( σ ( y ) x + ( 1 - σ ( y ) ) y ) = τ ( y ) f ( x ) + ( 1 - τ ( y ) ) f ( y ) for $${x, y \in [0, \infty)}$$ x , y ∈ [ 0 , ∞ ) , $${x \geq y}$$ x ≥ y , where $${f : [0, \infty) \to \mathbb{R}}$$ f : [ 0 , ∞ ) → R and $${\sigma, \tau : [0, \infty)\to [0, 1]}$$ σ , τ : [ 0 , ∞ ) → [ 0 , 1 ] ; and $$F(\sigma(y)x + (1 - \sigma(y))y) = \tau(y)F(x) + (1 - \tau(y))F(y)$$ F ( σ ( y ) x + ( 1 - σ ( y ) ) y ) = τ ( y ) F ( x ) + ( 1 - τ ( y ) ) F ( y ) for $${x, y \in \mathcal{C}}$$ x , y ∈ C , $${x - y \in \mathcal{C}}$$ x - y ∈ C , where $${\mathcal{C}}$$ C is a convex cone in a real linear space, $${F : \mathcal{C} \to \mathbb{R}}$$ F : C → R and $${\sigma, \tau : \mathcal{C} \to [0, 1]}$$ σ , τ : C → [ 0 , 1 ] . We determine the solutions of these equations satisfying some natural regularity assumptions. In this way we generalize the result of J. Aczél and R. D. Luce. The Author(s), 2014 Composite equation nationallicence convex cone nationallicence continuity on rays nationallicence Aequationes mathematicae Springer Basel 89/2(2015-04-01), 355-365 0001-9054 89:2<355 2015 89 10 https://doi.org/10.1007/s00010-014-0297-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0297-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Chudziak Jacek Faculty of Mathematics and Natural Sciences, University of Rzeszów, Prof. St. Pigonia 1, 35-310, Rzeszów, Poland aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/2(2015-04-01), 355-365 0001-9054 89:2<355 2015 89 10