Some remarks on the Daróczy equation


The general solution of the functional equation
f(x) = f(x+1) + f(x(x+1)),
considered both on (0,+∞) and ℝ, are studied. Constructions of odd and even solutions are given.

1. K. Baron, P283R2, Aequationes Math. 35 (1988), 301-303.
2. K. Baron, On a problem of Z. Daróczy, Zeszyty Naukowe Pol. Śl. Z. 64 (1990), 51-54.
3. Z. Daróczy, P283, Aequationes Math. 32 (1987), 136-137.
4. W. Jarczyk, On a problem of Z. Daróczy, Ann. Math. Sil. 5 (1991), 83-90.
5. M. Laczkovich, R. Redheffer, Oscillating solutions of integral equations and linear recursion, Aequationes Math. 41 (1991), 13-32.
6. Z. Moszner, P283R1, Aequationes Math. 32 (1987), 146.

Published : 1995-09-29

BartłomiejczykL. (1995). Some remarks on the Daróczy equation. Annales Mathematicae Silesianae, 9, 47-63. Retrieved from

Lech Bartłomiejczyk 
Instytut Matematyki, Uniwersytet Śląski w Katowicach  Poland

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