Hyers–Ulam Stability of Symmetric Biderivations on Banach Algebras

Jung Rye Lee (), Choonkil Park () and Themistocles M. Rassias ()
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Jung Rye Lee: Daejin University
Choonkil Park: Hanyang University
Themistocles M. Rassias: National Technical University of Athens

A chapter in Mathematical Analysis in Interdisciplinary Research, 2021, pp 555-572 from Springer

Abstract: Abstract In C. Park (Indian J Pure Appl Math 50:413–426, 2019), Park introduced the following bi-additive s-functional inequality: 1 ∥ 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 ) , $$\displaystyle \begin{aligned} \begin {aligned}{} & \| f(x+y, z-w) + f(x-y, z+w) -2f(x, z)+2 f(y, w)\| \\ & \quad \le \left \|s \left (2f\left (\frac {x+y}{2}, z-w\right ) + 2f\left (\frac {x-y}{2}, z+w\right ) - 2f(x, z )+ 2 f(y, w)\right )\right \|, \end {aligned} {} \end{aligned} $$ where s is a fixed nonzero complex number with |s|

Date: 2021
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DOI: 10.1007/978-3-030-84721-0_24

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