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