Abstract
Existence theorems for and the determination of continuous solutions, defined on the real axis R, of the functional equationf (t)=A[t,f (at−b),f (at−c)], wherea, b, and c are real parameters, A:R×E×E → E is a continuous operator, and E is a Banach space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
G. E. Zhuravlev, Some Properties of Forgetting Automata, in: Problems in the Mathematical Analysis of Complex Systems [in Russian], Voronezh (1968), pp. 63–65.
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Moscow (1968).
A. I. Markushevich, The Theory of Analytic Functions [in Russian], Vol. 1, Moscow (1967).
V. S. Martynenko, Operational Calculus [in Russian], Kiev (1966).
V. A. Ditkin and A. P. Prudnikov, Operational Calculus [in Russian], Moscow (1966).
P. S. Aleksandrov, Introduction to the General Theory of Sets and Functions [in Russian], Moscow-Leningrad (1948).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 9, No. 2, pp. 161–170, February, 1971.
The author wishes to thank B. N. Sadovskii for his interest and help in this work.
Rights and permissions
About this article
Cite this article
Kozyakin, V.S. A functional equation. Mathematical Notes of the Academy of Sciences of the USSR 9, 95–100 (1971). https://doi.org/10.1007/BF01316987
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01316987