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Journal: Annales Mathematicae Silesianae

Stability of the Pexider functional equation

Roman Badora , Barbara Przebieracz , Peter Volkmann

Language: EN | Published: 30-09-2010 | Abstract | pp. 7-13

A stability result for the Pexider equation will be derived from a stability theorem published in [9] for the Cauchy functional equation. Then we discuss the quality of some constants occuring in this context; as a model case we consider functions defined on the multiplicative semigroup {1, 0}.

2010-09-30



Journal: Annales Mathematicae Silesianae

The stability of the Pexider equation

Kazimierz Nikodem

Language: EN | Published: 30-09-1991 | Abstract | pp. 91-93

A stability theorem for the Pexider functional equation (1) is proved. It is an analogue of the classical theorem of Hyers [5] relating to the stability of the Cauchy functional equation.

1991-09-30



Journal: Annales Mathematicae Silesianae

Connections between the completion of normed spaces over non-archimedean fields and the stability of the Cauchy equation

Jens Schwaiger

Language: EN | Published: 08-05-2020 | Abstract | pp. 151-163

In [12] a close connection between stability results for the Cauchy equation and the completion of a normed space over the rationals endowed with the usual absolute value has been investigated. Here similar results are presented when the valuation of the rationals is a p-adic valuation. Moreover a result by Zygfryd Kominek ([5]) on the stability of the Pexider equation is
formulated and proved in the context of Banach spaces over the field of p-adic numbers.

2020-05-08