Glasnik Matematicki, Vol. 50, No. 1 (2015), 77-99.

ON APPROXIMATE GENERALIZED LIE DERIVATIONS

Janusz Brzdęk and Ajda Fošner

Faculty of Management, University of Primorska, Cankarjeva 5, SI-6104 Koper, Slovenia
e-mail: ajda.fosner@fm-kp.si

Abstract.   Motivated by the notion of the Hyers-Ulam stability, we prove results that are efficient tools for the study of approximate generalized Lie derivations on Lie algebras. We also provide simple examples of applications of our outcomes. In particular, we obtain some auxiliary results on the stability of the additive Cauchy equation.

2010 Mathematics Subject Classification.   16W20, 16W25, 39B62, 39B82.

Key words and phrases.   Stability, normed algebra, Banach bimodule, Lie derivation, generalized Lie derivation.

DOI: 10.3336/gm.50.1.07

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