Permuting Triderivations and Permuting Trihomomorphisms in Complex 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 283-302 from Springer

Abstract: Abstract Park (Permuting triderivations and permuting trihomomorphisms in Banach algebras, preprint) introduced the following tri-additive s-functional inequality 1 ∥ f ( x + y , z − w , a + b ) + f ( x − y , z + w , a − b ) −2 f ( x , z , a ) + 2 f ( x , w , b ) −2 f ( y , z , b ) + 2 f ( y , w , a ) ∥ ≤ s 2 f x + y 2 , z − w , a + b + 2 f x − y 2 , z + w , a − b −2 f ( x , z , a ) + 2 f ( x , w , b ) −2 f ( y , z , b ) + 2 f ( y , w , a ) , $$\displaystyle \begin{aligned} \begin{array}{rcl} {} & &\displaystyle \| f(x+y, z-w, a+b) + f(x-y, z+w, a-b) \\ & &\displaystyle \qquad -2 f(x, z, a) + 2 f(x, w, b) -2f(y, z, b) +2 f(y, w, a)\| \\ & &\displaystyle \quad \le \left\| s \left(2f\left(\frac{x+y}{2}, z-w, a+b \right) + 2f\left(\frac{x-y}{2}, z+w, a-b\right) \right. \right. \\ & &\displaystyle \qquad \left. \left. -2 f(x, z, a) + 2 f(x, w, b) -2f(y, z, b) +2 f(y, w, a)\right)\right\| , \end{array} \end{aligned} $$ where s is a fixed nonzero complex number with | s |

Date: 2026
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DOI: 10.1007/978-3-032-08949-6_13

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