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On a New Approach for Stability and Controllability Analysis of Functional Equations

Author

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  • Safoura Rezaei Aderyani

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran)

  • Reza Saadati

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, Iran)

  • Donal O’Regan

    (School of Mathematical and Statistical Sciences, University of Galway, H91 TK33 Galway, Ireland)

  • Chenkuan Li

    (Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada)

Abstract

We consider a new approach to approximate stability analysis for a tri-additive functional inequality and to obtain the optimal approximation for permuting tri-derivations and tri-homomorphisms in unital matrix algebras via the vector-valued alternative fixed-point theorem, which is a popular technique of proving the stability of functional equations. We also present a small list of aggregation functions on the classical, well-known special functions to investigate the best approximation error estimates using a different concept of perturbation stability.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3458-:d:1213910
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    References listed on IDEAS

    as
    1. Nicole Brillouët-Belluot & Janusz Brzdęk & Krzysztof Ciepliński, 2012. "On Some Recent Developments in Ulam's Type Stability," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-41, December.
    2. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    3. 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.
    4. Sivashankar, M. & Sabarinathan, S. & Nisar, Kottakkaran Sooppy & Ravichandran, C. & Kumar, B.V. Senthil, 2023. "Some properties and stability of Helmholtz model involved with nonlinear fractional difference equations and its relevance with quadcopter," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    5. Choonkil Park & Abbas Najati, 2007. "Homomorphisms and Derivations in C * -Algebras," Abstract and Applied Analysis, Hindawi, vol. 2007, pages 1-12, April.
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    Keywords

    multi stability; approximation;

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