Mathematics (all); Discrete Mathematics and Combinatorics; Applied Mathematics; General Mathematics
Abstract :
[en] In this work, we present the Cauchy functional equation in the context of connected Lie groups. We consider two generalizations of this equation with higher orders of the finite difference.
Disciplines :
Mathematics
Author, co-author :
Molla, Arman ; Université de Liège - ULiège > Mathematics
Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
The monomial functional equation for connected Lie groups
J. Aczél J. Dhombres Functional Equations in Several Variables 1989 Cambridge Cambridge University Press 10.1017/CBO9781139086578
J. Brzdȩk Remarks on hyperstability of the Cauchy functional equation Aequ. Math. 2013 86 255 267 3127008 10.1007/s00010-012-0168-4
J. Brzdȩk E. El-hady On hyperstability of the Cauchy functional equation in n-Banach spaces Mathematics 2020 8 1886 10.3390/math8111886
A.-L. Cauchy Cours d’Analyse de l’École Royale Polytechnique 1821 Paris Debure frères
G. Darboux Mémoire sur les fonctions discontinues Ann. Sci. de l’Ecole Norm. Superieure 1875 4 57 112 1508624 10.24033/asens.122
A. Gilányi Hyers–Ulam stability of monomial functional equations on a general domain Proc. Natl. Acad. Sci. U.S.A. 1999 96 10588 10590 1712533 10.1073/pnas.96.19.10588
S.M. Jung D. Popa M.T. Rassias On the stability of the linear functional equation in a single variable on complete metric groups J. Glob. Optim. 2014 59 165 171 3182526 10.1007/s10898-013-0083-9
E.L. Koh The Cauchy functional equations in distributions Proc. Am. Math. Soc. 1989 106 641 646 942634 10.1090/S0002-9939-1989-0942634-7
R. Kucharski R. Łukasik The form of multi-additive symmetric functions Results Math. 2018 73 150 15 3867628
Kuczman, M.: An Introduction to the Theory of Functional Equations and Inequalities: Cauchy’s Equation and Jenssen’s Inequality. Basel, Birkäuser (2008)
A. Molla S. Nicolay The Fréchet functional equation for Lie groups Mediterr. J. Math. 2021 18 1 18 10.1007/s00009-021-01701-z
A. Molla S. Nicolay J.-P. Schneiders On some generalizations of the Fréchet functional equations J. Math. Anal. Appl. 2018 466 1400 1409 3825447 10.1016/j.jmaa.2018.06.058
D. Reem Remarks on the Cauchy functional equation and variations of it Aequ. Math. 2017 91 237 264 3627381 10.1007/s00010-016-0463-6
H. Stetkær Functional Equations on Groups 2013 Singapore World Scientific 10.1142/8830
Szekelyhidi, L.: Convolution Type Functional Equations on Topological Abelian Groups. World Scientific Publishing Company, London (1991)