Bi-quadratic Derivations and Bi-quadratic Homomorphisms 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 341-350 from Springer

Abstract: Abstract In this paper, we solve the following bi-quadratic s-functional inequality 1 ∥ f ( x + y , z + w ) + f ( x + y , z − w ) + f ( x − y , z + w ) + f ( x − y , z − w ) −4 [ f ( x , z ) + f ( y , z ) + f ( x , w ) + f ( y , w ) ] ∥ ≤ ∥ s ( f ( x + y , z ) + f ( x − y , z ) + f ( x + y , w ) + f ( x − y , w ) − f ( x , z + w ) − f ( x , z − w ) − f ( y , z + w ) − f ( y , z − w ) ) ∥ , $$\displaystyle \begin{array}{@{}rcl@{}} {} && \|f(x+y,z+w)+f(x+y,z-w)+f(x-y,z+w)+f(x-y,z-w)\\ && \quad - 4[f(x,z)+f(y,z)+f(x,w)+f (y,w)]\| \\ && \le \|s (f(x+y,z)+f(x-y,z)+f(x+y,w)+f(x-y,w)\\&& \quad -f(x,z+w)-f(x,z-w)-f(y,z+w)-f(y,z-w))\| , \end{array} $$ where s is a fixed nonzero real or complex number with | s |

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-08949-6_16

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DOI: 10.1007/978-3-032-08949-6_16

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