C ∗ $$C^{\ast }$$ -Ternary Biderivations and C ∗ $$C^{\ast }$$ -Ternary Bihomomorphisms

Jung Rye Lee (), Choonkil Park () and Michael Th. Rassias
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Jung Rye Lee: Daejin University
Choonkil Park: Hanyang University
Michael Th. Rassias: Hellenic Military Academy

A chapter in Geometry and Non-Convex Optimization, 2025, pp 279-292 from Springer

Abstract: Abstract Using the direct method, we prove the Hyers-Ulam stability of C ∗ $$C^*$$ -ternary biderivations and C ∗ $$C^*$$ -ternary bihomomorphism in C ∗ $$C^*$$ -ternary algebras, associated with the following bi-additive s-functional inequality: ∥ 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 ) , $$\displaystyle \begin {aligned}{} && \| f(x+y, z-w) + f(x-y, z+w) -2f(x,z)+2 f(y, w)\| \\ && \le \left \| s \left (2f\left (\frac {x+y}{2}, z-w\right ) + 2f\left (\frac {x-y}{2}, z+w\right ) - 2f(x,z )+ 2 f(y, w)\right )\right \|, \end {aligned} $$ where s is a fixed nonzero complex number with | s |

Date: 2025
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DOI: 10.1007/978-3-031-87057-6_11

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