On the stability of higher ring left derivations

Yong-Soo Jung ()
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Yong-Soo Jung: Sun Moon University

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 3, 523-533

Abstract: 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: $${h_n}\left( {xy} \right) = \sum\limits_{\begin{array}{*{20}{c}} {i + j = n} \\ {i \leqslant j} \end{array}} {\left[ {{h_i}\left( x \right){h_j}\left( y \right) + {c_{ij}}{h_i}\left( y \right){h_j}\left( x \right)} \right]} $$ h n ( x y ) = ∑ i + j = n i ≤ j [ h i ( x ) h j ( y ) + c i j h i ( y ) h j ( x ) ] , where $${c_{ij}} = \left\{ {\begin{array}{*{20}{c}} 1&{if\;i \ne j,} \\ 0&{if\;i = j.} \end{array}} \right.$$ c i j = { 1 i f i ≠ j , 0 i f i = j .

Keywords: Higher left ring derivation; approximately higher left ring derivation; stability (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0201-8

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