On some solutions of the Schröder equation in Banach spaces
Abstract
The aim of this paper is to prove results on solutions of the Schröder equation (1) defined on cones in Banach spaces and having some properties connected with monotonicity and boundedness.
References
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2. A. Joffe, F. Spitzer, On multitype branching processes with ρ ≤ 1, J. Math. Anal. Appl. 19 (1967), 409-430.
3. H.G. Krein, M.A. Rutman, Linear operators leaving invariant a cone in a Banach space, Uspehi Matematičeskih Nauk (N.S.) 3, no. 1 (23) (1948), 3-95. [English translation: Functional Analysis and Measure Theory, American Mathematical Society Translations - Series 1, vol. 10, 1962].
4. M. Kuczma, Functional equations in a single variable, Monografie Matematyczne 46, PWN, Warszawa 1968.
5. M. Kuczma, B. Choczewski, R. Ger, Iterative Functional Equations, Encyclopedia of mathematics and its applications 32, Cambridge University Press 1990.
WalorskiJ. (1994). On some solutions of the Schröder equation in Banach spaces. Annales Mathematicae Silesianae, 8, 103-110. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14222
Janusz Walorski
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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