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Superstability for generalized module left derivations and generalized module derivations on a Banach module. II. (English) Zbl 1211.39015

[For part I see J. Inequal. Appl. 2009, Article ID 718020, 10 p. (2009; Zbl 1185.46033).] Motivated by some recent results of S.-Y. Kang and I.-S. Chang [Abstr. Appl. Anal. 2008, Article ID 915292 (2008; Zbl 1160.47031)] who obtained the superstability of generalized left derivations and generalized derivations, the authors of the present paper investigate the superstability of generalized module left derivations and generalized module derivations on a Banach module.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
47B47 Commutators, derivations, elementary operators, etc.
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