Authors: Davidov, Sergey
Krapež, Aleksandar 
Movsisyan, Yuri
Title: Functional equations with division and regular operations
Journal: Asian-European Journal of Mathematics
Volume: 11
Issue: 3
Issue Date: 1-Jun-2018
ISSN: 1793-5571
DOI: 10.1142/S179355711850033X
Functional equations are equations in which the unknown (or unknowns) are functions. We consider equations of generalized associativity, mediality (bisymmetry, entropy), paramediality, transitivity as well as the generalized Kolmogoroff equation. Their usefulness was proved in applications both in mathematics and in other disciplines, particularly in economics and social sciences (see J. Aczél, On mean values, Bull. Amer. Math. Soc. 54 (1948) 392-400; J. Aczél, Remarques algebriques sur la solution donner par M. Frechet a l'equation de Kolmogoroff, Pupl. Math. Debrecen 4 (1955) 33-42; J. Aczél, A Short Course on Functional Equations Based Upon Recent Applications to the Social and Behavioral Sciences, Theory and decision library, Series B: Mathematical and statistical methods (D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1987); J. Aczél, Lectures on Functional Equations and Their Applications (Supplemented by the author, ed. H. Oser) (Dover Publications, Mineola, New York, 2006); J. Aczél, V. D. Belousov and M. Hosszu, Generalized associativity and bisymmetry on quasigroups, Acta Math. Acad. Sci. Hungar. 11 (1960) 127-136; J. Aczél and J. Dhombres, Functional Equations in Several Variables (Cambridge University Press, New York, 1991); J. Aczél and T. L. Saaty, Procedures for synthesizing ratio judgements, J. Math. Psych. 27(1) (1983) 93-102). We use unifying approach to solve these equations for division and regular operations generalizing the classical quasigroup case.
Keywords: Associative | epitopic | homotopic | hyperidentity | Kolmogoroff equation | medial | paramedial | transitive
Publisher: World Scientific
Project: Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 
Representations of logical structures and formal languages and their application in computing 
State Committee of Science of the Republic of Armenia, Grant Nos. 10-3/1-41 and 15T-1A258

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