On the alienation of the Cauchy equation and the Lagrange equation

Troczka-Pawelec, Katarzyna; Tyrala, Iwona

doi:10.16926/m.2016.21.09

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Cited by 6 publications

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“…, m and let functions f, g be defined on X and take values in Y. For a l,k , b l,k given by (17) and (18) we define the sets A l , B l by the formulas:…”

Section: Lemmamentioning

confidence: 99%

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Alienation of two general linear functional equations

Szostok

2019

Aequat. Math.

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We study the alienation problem for two general linear equations i.e. we compare the solutions of the system of equations n i=1 α i f (p i x + q i y) = 0 m j=1 β j g(s j x + t j y) = 0 with the solutions of the single equation n i=1 α i f (p i x + q i y) = m j=1 β j g(s j x + t j y). To this end we introduce the notion of l-alienation-alienation in the class of monomial functions of order l. We use our results among others to study the alienation properties of two monomial functional equations.

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“…, m and let functions f, g be defined on X and take values in Y. For a l,k , b l,k given by (17) and (18) we define the sets A l , B l by the formulas:…”

Section: Lemmamentioning

confidence: 99%

“…Then the problem of alienation was studied by many authors, we cite here just some of them [2][3][4]6,9,11,13,17], for the more detailed study of the history and present state of this problem see [7].…”

Section: Introductionmentioning

confidence: 99%