Hyers–Ulam Stability of an Additive-Quadratic Functional Equation

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 Approximation and Computation in Science and Engineering, 2022, pp 561-572 from Springer

Abstract: Abstract Using the fixed point method and the direct method, we prove the Hyers–Ulam stability of Lie biderivations and Lie bihomomorphisms in Lie Banach algebras, associated with the bi-additive 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 ) ∥ ≤ s 2 f x + y , z − w + 2 f x − y , z + w − 4 f ( x , z ) + 4 f ( y , w ) , $$\displaystyle \begin{aligned} & \| f(x+y, z+w) + f(x+y, z-w) + f(x-y, z+w) \\ &\qquad + f(x-y, z-w) -4f(x,z)\| \\ & \quad \le \left \|s \left (2f\left (x\kern -0.7pt+\kern -0.7pt y, z\kern -0.7pt-\kern -0.7pt w\right ) \kern -0.7pt+\kern -0.7pt 2f\left (x-y, z\kern -0.7pt+\kern -0.7pt w\right ) \kern -0.7pt-\kern -0.7pt 4f(x,z )\kern -0.7pt+\kern -0.7pt 4 f(y, w)\right )\right \|, \end{aligned} $$ where s is a fixed nonzero complex number with |s|

Keywords: Hyers–Ulam stability; Mixed type functional equation; Banach space; Fuzzy Banach space; Fixed point method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/978-3-030-84122-5_29

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