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Pexider type equation on a region

Chudziak M., Sobek B.

Journal of Applied Analysis

2017

Vol. 23, nr 2

101--110

We consider the problem of existence and uniqueness of extensions for the solutions of the Pexider type equation f(x + y) = g(x) + h(y) + k(x)l(y) for (x, y) ∈ D, where X is a normed space and D is a nonempty open and connected subset of X2.

A note on stability of the popoviciu functional equation on restricted domain

Brzdęk J.

Demonstratio Mathematica

2010

Vol. 43, nr 3

635-641

We prove the Hyers-Ulam stability, on restricted domain, of a functional equation of Jensen type, introduced by T. Popoviciu (1965).