Lie Bracket Derivation-Derivations in Banach Algebras

Jung Rye Lee (), Choonkil Park () and Michael Th. Rassias
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Jung Rye Lee: Daejin University, Department of Data Science
Choonkil Park: Hanyang University, Department of Mathematics
Michael Th. Rassias: Hellenic Military Academy, Department of Mathematics and Engineering Sciences

A chapter in Functional Equations and Ulam’s Problem, 2026, pp 327-339 from Springer

Abstract: Abstract In this paper, we introduce and solve the following additive-additive ( s , t ) $$(s,t)$$ -functional inequality 1 ∥ g x + y − g ( x ) − g ( y ) ∥ + ∥ h ( x + y ) + h ( x − y ) −2 h ( x ) ∥ ≤ s 2 g x + y 2 − g ( x ) − g ( y ) + t 2 h x + y 2 + 2 h x − y 2 −2 h ( x ) , $$\displaystyle \begin{aligned} \begin{array}{rcl} {} & &\displaystyle \|g\left(x+y\right) -g(x) -g(y)\| +\| h(x+y) + h(x-y) -2 h(x) \| \\ & &\displaystyle \quad \le \left\|s\left( 2 g\left(\frac{x+y}{2}\right)-g(x)-g(y)\right)\right\| \\ & &\displaystyle \qquad + \left\|t \left( 2h\left(\frac{x+y}{2}\right)+ 2h \left(\frac{x-y}{2}\right)- 2h (x)\right) \right\| , \end{array} \end{aligned} $$ where s and t are fixed nonzero complex numbers with | s |

Date: 2026
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DOI: 10.1007/978-3-032-08949-6_15

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