References

References

 [1]

J. Aczél and D. Gronau. Some differential equations related to iteration theory. Can. J. Math., XL(3):695-717, 1988.

 [2]

J. Aczél. Lectures on functional equations and its applications. Academic Press, New York, London, 1966.

 [3]

L. Berg and D. Gronau. Asymptotische Lösungen der Translationsgleichung. Results in Mathematics, 26:215-220, 1994.

 [4]

L. Berg and D. Gronau. Erratum zu: Asymptotische Lösungen der Translationsgleichung. Results in Mathematics, 27:422-423, 1995.

 [5]

L. Berg. Asymptotic properties of the translation equation. In J.P. Lampreia et al., editors, European Conference on ITERATION THEORY (ECIT 1991), pages 22-26, Singapore, New Jersey, London, Honkong, 1992. World Scientific.

 [6]

G.D. Birkhoff. Surface Transformations and Their Dynamical Applications. Acta Math., 43:1-119, 1922.

 [7]

J. Birkl. Asymptotische Formeln der Iterierten einer Funktion. Master's thesis, Institut für Mathematik der KFU-Graz, 1997.

 [8]

P.M. Cohn. Algebra, volume 3. J. Wiley & Sons, Chichester etc., 2nd edition, 1991.

 [9]

I. Fenyö and G.L. Forti. On the inhomogeneous Cauchy functional equation. Stochastica, 5:71-77, 1981.

 [10]

G.L. Forti. An existence and stability theorem for a class of functional equations. Stochastica, 4:23-30, 1980.

 [11]

G.L. Forti. Hyers-Ulam stability of functional equations in several variables. Aequationes Mathematicae, 50:143-190, 1995.

 [12]

D. Gronau. Do the Jabotinsky equations imply the translation equation. In C. Alsina, Libre J., et al., editors, European Conference on Iteration Theory (ECIT 87), pages 231-239, Singapore, 1989. World Scientific Publ. Co.

 [13]

D. Gronau. The Jabotinsky equations and the embedding problem. In Ch. Mira, N. Netzer, C. Simó, and Gy. Targonski, editors, European Conference on ITERATION THEORY, pages 138-147, Singapore, 1991. World Scientific.

 [14]

D. Gronau. On the structure of the solutions of the Jabotinsky equations in Banach spaces. Z. Anal. Anw., 10(3):335-343, 1991.

 [15]

D. Gronau. An asymptotic formula for the iterates of a function. Results in Math., 23:49-54, 1993.

 [16]

D. Gronau. An asymptotic formula for the iterates of a function and related functional equations. In European Conference on ITERATION THEORY (ECIT 1992), Singapore, New Jersey, London, Honkong, 1996. World Scientific.

 [17]

G. Guzik. On embedding of a linear functional equation. Wyz Szkola Ped. Kraków Rocznik Nauk.-Dydact. Prace Matematyczne, 16:23-33, 1999.

 [18]

F. Halter-Koch and L. Reich. Charakterisierung von Derivationen höherer Ordnung mittels Funktionalgleichungen. Sitzungsberichte ÖAW, Math.-nat. Kl. Abt. II, 207:123-131, 1998.

 [19]

F. Halter-Koch and L. Reich. Additive functions commuting with Möbius transformations and field homomorphisms. Aequationes Mathematicae, 58:176-182, 1999.

 [20]

F. Halter-Koch and L. Reich. Characterization of field homomorphisms by functional equations. To appear in Publ. Math. Debrecen, 1999.

 [21]

F. Halter-Koch. Characterization of field homomorphisms and derivations by functional equations. To appear in Aequationes mathematicae, 1999.

 [22]

M. Kuczma, B. Choczewski, and R. Ger. Iterative Functional Equations, volume 32 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1990.

 [23]

M. Kuczma. Functional equations in a single variable, volume 46 of Monografie Math. Polish Scientific Publishers, Warsaw, 1968.

 [24]

G. Mehring. Iteration im Ring der formalen Potenzreihen ohne Regularitätsvoraussetzungen. Ber. Math.-Stat. Sekt. Forschungszent. Graz, 265, 1986.

 [25]

Z. Moszner. General theory of the translation equation. Aequationes Mathematicae, 50:17-37, 1995.

 [26]

Z. Moszner. Sur le prolongement covariant d'une équation linéare par rapport au groupe d'itération. Sitzungsberichte ÖAW, Math.-nat. Kl. Abt. II, 207:173-182, 1999.

 [27]

Z. Moszner. Les équations de pré-Schröder. Submitted to Annales Mathematicae Silesianae.

 [28]

L. Reich and J. Schwaiger. Über einen Satz von Shl. Sternberg in der Theorie der analytischen Iterationen. Mh. Math., 83:207-221, 1977.

 [29]

L. Reich and J. Schwaiger. Über die Funktionalgleichung N o T=T o M für formale Potenzreihen. Aequationes Mathematicae, 19:66-78, 1979.

 [30]

L. Reich and J. Schwaiger. Linearisierung formal-biholomorpher Abbildungen und Iterationsprobleme. Aequationes Mathematicae, 20:224-243, 1980.

 [31]

L. Reich. Über die allgemeine Lösung der Translationsgleichung in Potenzreihenringen. Berichte der Math.-statistischen Gesellschaft im Forschungszentrum Graz, 159, 1981.

 [32]

L. Reich. Kontinuierliche Iteration formal-biholomorpher Abbildungen und Differenzenrechnung. Abh. Mathem. Sem. Univ. Hamburg, 52, 1982.

 [33]

L. Reich. On a differential equation arising in iteration theory in rings of formal power series in one variable. In R. Liedl, L. Reich, and Gy. Targonsky, editors, Iteration Theory and its Functional Equations, volume 1163 of Lecture Notes in Mathematics, pages 135-148. Springer, 1985.

 [34]

L. Reich. Holomorphe Lösungen der Differentialgleichung von E. Jabotinsky. (Prof. E. Hlawka zum 70. Geburtstag). Sitzungsbericht der Österr. Akademie der Wissenschaften, Math.-naturwiss. Klasse, Abt. II, 195:157-166, 1986.

 [35]

L. Reich. On Families of Commuting Formal Power Series. Berichte der Mathematisch-statistischen Sektion der Forschungsgesellschaft Joanneum Graz, 294:1-18, 1988.

 [36]

L. Reich. Iteration of Automorphisms of Formal Power Series Rings and of Complete Local Rings. In C. Alsina et al., editors, European Conference on Iteration Theory 1987, pages 26-41, Singapore, New Jersey, London, Hong Kong, 1989. World Scientific.

 [37]

L. Reich. Iterative roots and families of commuting formal power series. Annales Mathematicae Silesianae, 8:189-201, 1994.

 [38]

L. Reich. 24. remark in the thirty-fifth international symposium on functional equations, september 7-14, 1997, graz-mariatrost, austria. Aequationes Mathematicae, 55:281-318, 1998.

 [39]

L. Reich. Derivationen zweiter Ordnung als Lösungen von Funktionalgleichungen. Grazer Math. Ber., 337:45-65, 1998.

 [40]

L. Reich. Remark (introducing pre-linear equations). Aequationes Mathematicae, 55:296-297, 1998.

 [41]

J. Schwaiger and H. Fripertinger. Some applications of functional equations in astronomy. To be published.

 [42]

J. Schwaiger. On the stability of derivations of higher order. To be published in Rocznik Nauk.-Dydact. WSP w Krokowie Prace Matematyczne.

 [43]

S. Sternberg. Infinite Lie Groups and Formal Aspects of Dynamical Systems. J. Math. Mech., 10:451-474, 1961.

 [44]

Gy. Targonski. Problem (P63). Aequationes Mathematicae, 4:251, 1970.

 [45]

Gy. Targonski. Topics in Iteration Theory. Studia Mathematica, Skript 6. Vandenhoeck & Ruprecht, Göttingen, Zürich, 1981.

 [46]

Gy. Targonski. Progress of iteration theory since 1981. Aequationes Mathematicae, 50:50-72, 1995.

References