Duplicating the cube and functional equations
type: Item
instance of: scholarly article
title: Duplicating the cube and functional equations
zbMATH Open document ID: 0829.39008
DOI: 10.1007/BF03323055
author: Witold Jarczyk
author: Maciej Sablik
published in: Results in Mathematics
publication date: 1995-08-15T00:00:00Z
review text: The authors make some interesting contributions to the study of the system of functional equations \[ f \bigl( px + (1 - p)y \bigr) f \bigl( (1 - p)x + py \bigr) = f(x) \cdot f(y), \tag{1} \] \[ f(x)f \bigl( px + (1 - p)y \bigr) + f(y)f \bigl( (1 - p)x + py \bigr) = f \bigl( px + (1 - p)y \bigr)^2 + f \bigl( (1 - p)x + py \bigr)^2. \tag{2} \] These equations were introduced by C. Alsina and J. L. Garcia-Roig in relation with the study of some results of G. de Saint Vincent related to the classical Greek problem of duplicating the cube. In this paper equations (1) and (2) are solved (jointly or separated) under different regularity conditions and for different values of \(p\) \((p \neq 1/3;\;p = 1/3;\;p \in Q; \ldots)\). In the restricted domain \(y = 2x\) the equations are investigated with detail.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B62
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 785177
zbMATH Keywords: system of functional equations
zbMATH Keywords: duplicating the cube
zbMATH Keywords: restricted domain
MaRDI profile type: Publication
cites work: On two functional equations related to a result of Grégoire de Saint-Vincent
cites work: Q3808598
cites work: Q4002346
cites work: Non-Negative Measurable Solutions of Difference Equations
cites work: Q4006638
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description: scientific article; zbMATH DE number 785177