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Superstability of Generalized Module Left Higher Derivations on a Multi-Banach Module

In: Handbook of Functional Equations

Author

Listed:
  • T. L. Shateri

    (Department of Mathematics and Computer Sciences)

  • Z. Afshari

    (Department of Mathematics and Computer Sciences)

Abstract

The problem of stability of functional equations was originally raised by Ulam in 1940. During the last decades, several stability problems for various functional equations have been investigated by several authors. In this chapter, by defining a multi-Banach space, we introduce a multi-Banach module. Also, we define the notion of generalized module left higher derivations and approximate generalized module left higher derivations. Then, we discuss the superstability of an approximate generalized module left higher derivation on a multi-Banach module. In fact, we show that an approximate generalized module left higher derivation on a multi-Banach module is a generalized module left higher derivation. Finally, we get the similar result for a linear generalized module left higher derivation.

Suggested Citation

  • T. L. Shateri & Z. Afshari, 2014. "Superstability of Generalized Module Left Higher Derivations on a Multi-Banach Module," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Handbook of Functional Equations, edition 127, pages 353-365, Springer.
    • Handle: RePEc:spr:spochp:978-1-4939-1286-5_16
    DOI: 10.1007/978-1-4939-1286-5_16
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