On Solutions of Some Generalizations of the Goła̧b–Schinzel Equation

Jabłońska, Eliza

doi:10.1007/978-1-4614-0055-4_32

Cited by 10 publications

(8 citation statements)

References 44 publications

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“…and some other equations related to it. A survey on superstability results for such equations can be found in [3, pages 29-32] (for more information and further references on those equations see also [62]).…”

Section: Superstabilitymentioning

confidence: 99%

Hyperstability and Superstability

Brzdęk

Ciepliński

2013

Abstract and Applied Analysis

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Section: Superstabilitymentioning

confidence: 99%

Hyperstability and Superstability

Brzdęk

Ciepliński

2013

Abstract and Applied Analysis

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“…As an immediate application of this framework, we can rephrase the Beurling asymptotics, clarifying the underlying cocycle structure. These, as we will see, lead to functional equations, whose solutions are discussed in §5 below -see also the surveys [Brz1] and [Jab5]; cf. [Ost1].…”

Section: Asymptotic Actions and Functional Equationsmentioning

confidence: 85%

General regular variation, Popa groups and quantifier weakening

Bingham

Ostaszewski

2020

Journal of Mathematical Analysis and Applications

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man and mathematician, who died with his boots on 'The soldiers' music and the rites of war Speak loudly for him.' (Shakespeare, Hamlet Act V.2) Abstract. We introduce general regular variation, a theory of regular variation containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. The unifying theme is the Popa groups of our title viewed as locally compact abelian ordered topological groups, together with their Haar measure and Fourier theory. The power of this unified approach is shown by the simplification it brings to the whole area of quantifier weakening, so important in this field.

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“…and proved that solutions of this equation can be described by solutions of a partially pexiderized Go lab-Schinzel equation 6) considered in several papers (a bibliography can be found in the survey paper [7]) and very recently in papers [1] and [10]. For the first time Eq.…”

Section: Introductionmentioning

confidence: 95%

“…It turned out that this equation and its generalizations have a lot of applications (an extensive bibliography concerning the Go lab-Schinzel equation, its generalizations and applications can be found in [2] and [7]). It is the main reason, why so numerous authors considered the equation and its generalizations under various assumptions.…”

Section: Introductionmentioning

confidence: 99%

On locally bounded above solutions of an equation of the Goła̧b–Schinzel type

Jabłońska

2013

Aequat. Math.

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Abstract. We characterize solutions f, g : R → R of the functional equation f (x + g(x)y) = f (x)f (y) under the assumption that f is locally bounded above at each point x ∈ R. Our result refers to Go lab and Schinzel (Publ Math Debr 6:113-125, 1959) and Wo lodźko (Aequationes Math 2: [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] 1968).Mathematics Subject Classification (2010). Primary 39B22; Secondary 26A03.

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On Solutions of Some Generalizations of the Goła̧b–Schinzel Equation

Cited by 10 publications

References 44 publications

Hyperstability and Superstability

Hyperstability and Superstability

General regular variation, Popa groups and quantifier weakening

On locally bounded above solutions of an equation of the Goła̧b–Schinzel type

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