Symmetric biderivations on Banach algebras

Choonkil Park ()
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Choonkil Park: Hanyang University

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 2, 413-426

Abstract: Abstract In [25], Park introduced the following bi-additive s-functional inequalities (1) $$\matrix{{{\rm{||}}f(x + y, z - w) + f(x - y, z + w) - 2f(x, z) + 2f(y, w){\rm{||}}} \hfill \cr {\;\;\;\; \le \left\| {s\left({2f\left({{{x + y} \over 2}, z - w} \right) + 2f\left({{{x - y} \over 2}, z + w} \right) - 2f(x, z) + 2f(y, w)} \right)} \right\|} \hfill \cr}$$ | | f ( x + y , z − w ) + f ( x − y , z + w ) − 2 f ( x , z ) + 2 f ( y , w ) | | ≤ ∥ s ( 2 f ( x + y 2 , z − w ) + 2 f ( x − y 2 , z + w ) − 2 f ( x , z ) + 2 f ( y , w ) ) ∥ and (2) $$\matrix{{\left\| {2f\left({{{x + y} \over 2}, z - w} \right) + 2f\left({{{x - y} \over 2}, z + w} \right) - 2f(x, z) + 2f(y, w)} \right\|} \hfill \cr {\;\; \le {\rm{||}}s(f(x + y, z - w) + f(x - y, z + w) - 2f(x, z) + 2f(y, w)){\rm{||,}}} \hfill \cr} $$ ∥ 2 f ( x + y 2 , z − w ) + 2 f ( x − y 2 , z + w ) − 2 f ( x , z ) + 2 f ( y , w ) ∥ ≤ | | s ( f ( x + y , z − w ) + f ( x − y , z + w ) − 2 f ( x , z ) + 2 f ( y , w ) ) | | , where s is a fixed nonzero complex number with |s|

Keywords: Symmetric biderivation on C* -algebra; skew-symmetric biderivation on C* -algebra; Hyers-Ulam stability; bi-additive s-functional inequality (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0335-6

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