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On some generalizations of Gołąb-Schinzel functional equation

Matkowski J., Okrzesik J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2010

Vol. 15

81--90

Composite functional equations in several variables generalizing the Gołąb-Schinzel equation are considerd and some simple methods allowing us to determine their one-to-one solutions, bijective solutions or the solutions having exactly one zero are presented. For an arbitrarily fixed real p, the functional equation Φ([pφ(y) + (1−p)]x +[(1−p)φ(x)+p]y) = φ(x)φ(y), x,y ∈ R, being a special generalization of the Gołąb-Schinzel equation, is considered.

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)).