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Hyers–Ulam Stability of an Additive-Quadratic Functional Equation

In: Approximation and Computation in Science and Engineering

Author

Listed:
  • Jung Rye Lee

    (Daejin University)

  • Choonkil Park

    (Hanyang University)

  • Themistocles M. Rassias

    (National Technical University of Athens)

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|

Suggested Citation

  • Jung Rye Lee & Choonkil Park & Themistocles M. Rassias, 2022. "Hyers–Ulam Stability of an Additive-Quadratic Functional Equation," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Approximation and Computation in Science and Engineering, pages 561-572, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84122-5_29
    DOI: 10.1007/978-3-030-84122-5_29
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    Cited by:

    1. Safoura Rezaei Aderyani & Reza Saadati & Donal O’Regan & Chenkuan Li, 2023. "On a New Approach for Stability and Controllability Analysis of Functional Equations," Mathematics, MDPI, vol. 11(16), pages 1-35, August.

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