Abstract
Functional equations are equations where the unknowns are functions. A well-known example of functional equation is the following Cauchy equation:
A function φ is a solution of this equation if, for any two values x and y, the application of φ to x + y equals the addition of the application of φ to x and to y. Therefore, the equation establishes conditions that functions φ have to satisfy. Typical solutions of this Cauchy equation are the functions φ(x) = αx for an arbitrary value for α.
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3.4 Bibliographical Notes
Aczél, J. (1961) Vorlesungen über Funktionalgleichungen und ihre Anwendungen, Birkhäuser Verlag.
Aczél, J. (1966) Lectures on Functional Equations and their Applications, Academic Press.
Aczél, J. (1987) A Short Course on Functional Equations, D. Reidel Publishing Company (Kluwer Academic Publishers Group).
Castillo, E., Cobo, A., Gutiérrez, J. M., Pruneda, R. E. (1999) Introducción a las redes funcionales con aplicaciones, Paraninfo.
Castillo, E., Cobo, A., Gutiérrez, J. M., Pruneda, R. E. (1999) Functional Networks with Applications. A Neural-Based Paradigm, Kluwer Academic Publishing.
Castillo, E., Ruiz-Cobo, M. R. (1992) Functional Equations and Modelling in Science and Engineering, Marcel Dekker, Inc.
Cauchy, A. L. (1821) Cours d’Analyse de l’Ecole Royale Polytechnique, Ire Partie, Analyse Algébraique, Paris.
Jensen, J. L.W. V. (1905) Om konvekse funktioner og uligheder imellem middelvaerier, Mat. Tidsskr, B 49–68.
Jensen, J. L. W. V. (1906) Sur les Fonctions Convexes et les Inégalités entre les Valeurs Moyennes, Acta Math. 30 175–193.
Legendre, A. M. (1791) Eléments de Géométrie. Note IV. Didot, Paris, 1791 (New York: Readex Microprint, 1970).
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(2007). Introduction to Functional Equations. In: Modeling Decisions. Cognitive Technologies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68791-7_3
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DOI: https://doi.org/10.1007/978-3-540-68791-7_3
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