On functional equation stemming from utility theory and psychophysics
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| 008 | 210128e20150401xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0297-z |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0297-z | ||
| 100 | 1 | |a Chudziak |D Jacek |u Faculty of Mathematics and Natural Sciences, University of Rzeszów, Prof. St. Pigonia 1, 35-310, Rzeszów, Poland |4 aut | |
| 245 | 1 | 0 | |a On functional equation stemming from utility theory and psychophysics |h [Elektronische Daten] |c [Jacek Chudziak] |
| 520 | 3 | |a 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. | |
| 540 | |a The Author(s), 2014 | ||
| 690 | 7 | |a Composite equation |2 nationallicence | |
| 690 | 7 | |a convex cone |2 nationallicence | |
| 690 | 7 | |a continuity on rays |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/2(2015-04-01), 355-365 |x 0001-9054 |q 89:2<355 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0297-z |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0297-z |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Chudziak |D Jacek |u Faculty of Mathematics and Natural Sciences, University of Rzeszów, Prof. St. Pigonia 1, 35-310, Rzeszów, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/2(2015-04-01), 355-365 |x 0001-9054 |q 89:2<355 |1 2015 |2 89 |o 10 | ||