### Remark on the Cauchy functional equation.

Svetozar Kurepa (1965)

Publications de l'Institut Mathématique [Elektronische Ressource]

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Svetozar Kurepa (1965)

Publications de l'Institut Mathématique [Elektronische Ressource]

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Andrzej Fryszkowski (1985)

Annales Polonici Mathematici

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Daróczy, Zoltán (1999)

Mathematica Pannonica

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Pl. Kannappan, M. Kuczma (1974)

Annales Polonici Mathematici

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Józef Tabor (1975)

Colloquium Mathematicae

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Marek Kuczma (1973)

Colloquium Mathematicae

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Z. Kamont (1977)

Annales Polonici Mathematici

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Palaniappan Kannappan (1995)

Mathware and Soft Computing

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Among normal linear spaces, the inner product spaces (i.p.s.) are particularly interesting. Many characterizations of i.p.s. among linear spaces are known using various functional equations. Three functional equations characterizations of i.p.s. are based on the Frchet condition, the Jordan and von Neumann identity and the Ptolemaic inequality respectively. The object of this paper is to solve generalizations of these functional equations.

Gian Luigi Forti (1980)

Stochastica

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Consider the class of functional equations g[F(x,y)] = H[g(x),g(y)], where g: E --> X, f: E x E --> E, H: X x X --> X, E is a set and (X,d) is a complete metric space. In this paper we prove that, under suitable hypotheses on F, H and ∂(x,y), the existence of a solution of the functional inequality d(f[F(x,y)],H[f(x),f(y)]) ≤ ∂(x,y), implies the existence of a solution of the above equation.

Maksimov, V.P., Munembe, J.S.P. (1997)

Memoirs on Differential Equations and Mathematical Physics

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A. Alexiewicz (1948)

Colloquium Mathematicae

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Halter-Koch, Franz (2000)

Mathematica Pannonica

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