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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Aequationes Mathemat...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Aequationes Mathematicae
Article . 1997 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1997
Data sources: zbMATH Open
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A package for symbolic solution of real functional equations of real variables

Authors: Castillo, Enrique; Iglesias, Andres;

A package for symbolic solution of real functional equations of real variables

Abstract

The authors describe a Mathematica package for the solution of functional equations. Solving functional equations is a tricky business. Most people working in the field have a bagful of equations whose solution is known and a bag of tricks (methods to reduce to these and thus solve other equations), nobody knows everything. Computers have better memories, so they can help if well programmed. The authors start with a database of ``the most important functional equations and their solutions for different domains and classes''. They also list ten methods of solution. While their names sound pretty general, in this reviewer's opinion this is an aspect which may need strengthening and considerably more work. At several places, e.g. p. 185, the authors speak about the ``same'' equation on different domains. This concept would have to be defined exactly. Another approach would be to ``computerize'' known solution methods for very large classes of equations. Several of these are algebraic or functional analytic, so there would be no need to restrict oneselves to real functions as the authors do. Examples of such methods are those of \textit{E. Vincze} [Publ. Math. 9, 149-163, 314-323 (1962); 10, 191-202, 283-318 (1963; Zbl 0125.35803)] and of \textit{L. Székelyhidi} [Convolution type functional equations on topological abelian groups (1991; Zbl 0748.39003)]. The first steps towards computerization of a generalization of the latter (in Maple) were made by \textit{A. Gilányi} [Charakterisierung von monomialen Funktionen und Lösung von Funktionalgleichungen mit Computern, Univ. Karlsruhe (1995)].

Country
Germany
Related Organizations
Keywords

admissible functions, functional equations, symbolic solution, Symbolic computation and algebraic computation, solution methods, Article, 510.mathematics, Functional equations for real functions, computerization, mathematica package

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green