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On the stability of higher ring left derivations

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Abstract

In this note, we investigate the Hyers-Ulam, the Isac and Rassias-type stability and the Bourgin-type superstability of a functional inequality corresponding to the following functional equation:

$${h_n}\left( {xy} \right) = \sum\limits_{\begin{array}{*{20}{c}} {i + j = n} \\ {i \leqslant j} \end{array}} {\left[ {{h_i}\left( x \right){h_j}\left( y \right) + {c_{ij}}{h_i}\left( y \right){h_j}\left( x \right)} \right]} $$

, where

$${c_{ij}} = \left\{ {\begin{array}{*{20}{c}} 1&{if\;i \ne j,} \\ 0&{if\;i = j.} \end{array}} \right.$$

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Correspondence to Yong-Soo Jung.

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Jung, Y. On the stability of higher ring left derivations. Indian J Pure Appl Math 47, 523–533 (2016). https://doi.org/10.1007/s13226-016-0201-8

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Key words

  • Higher left ring derivation
  • approximately higher left ring derivation
  • stability