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On new stability results for composite functional equations in quasi-β-normed spaces

Thanyacharoen Anurak, Sintunavarat Wutiphol

Demonstratio Mathematica

2021

Vol. 54, nr 1

68--84

In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation: f(f(x) – f(y)) = f(x + y) + f(x – y) – f(x) – f(y), where f maps from a(β, p)-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the composite s-functional inequality is discussed via our results.

A composite functional equation and invariant curves

Matkowski J., Okrzesik J.

Journal of Applied Analysis

2010

Vol. 16, nr 1

121-133

The continuous solutions of a composite functional equation are characterized. An applications to the problem of invariant curves is presented.

On the existence of Lipschitzian solution of a composite functional equation

Okrzesik J.

Demonstratio Mathematica

2006

Vol. 39, nr 1

97-100

There are presented conditions which guarantee the existence of a Lip- schitzian solution of the composite functional equation phi(x) = G (x,phi(H(x,phi(x)))) are presented.

On a composite functional equation

Matkowski J., Okrzesik J.

Demonstratio Mathematica

2003

Vol. 36, nr 3

653--658

We determine all continuous functions f : (0, oo) ->(0,oo) satisfying the functional equation f(xG(f(x)))=f(x)G(f(x)) where G is continuous and strictly increasing function such that 1 e G((0, oo)).