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Baire measurable solutions of a generalized Gołąb–Schinzel equation

100%

Jabłońska E.

Commentationes Mathematicae

2010

tom 50

nr 1

J. Brzdęk [1] characterized Baire measurable solutions \(f\colon X \to K\) of the functional equation \[ f (x + f (x)^n y) = f (x)f (y) \] under the assumption that \(X\) is a Fréchet space over the field \(K\) of real or complex numbers and \(n\) is a positive integer. We prove that his result holds even if \(X\) is a linear topological space over \(K\); i.e. completeness and metrizability are not necessary.

Functions having the Darboux property and satisfying some functional equation

100%

Jabłońska E.

Colloquium Mathematicum

2009

tom 114

nr 1

113-118

Let X be a real linear topological space. We characterize solutions f:X → ℝ and M:ℝ → ℝ of the equation f(x+M(f(x))y) = f(x)f(y) under the assumption that f and M have the Darboux property.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Commentationes Mathematicae

2 Jabłońska E.

1 2010

1 2009

Wyniki wyszukiwania

Baire measurable solutions of a generalized Gołąb–Schinzel equation

Functions having the Darboux property and satisfying some functional equation