IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i16p3458-d1213910.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/16/3458/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/16/3458/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Luca Anzilli & Silvio Giove, 2020. "Multi-criteria and medical diagnosis for application to health insurance systems: a general approach through non-additive measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 559-582, December.
    2. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2011. "Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes," Post-Print hal-00539032, HAL.
    3. Ya-Qiang Xu & Le-Sheng Jin & Zhen-Song Chen & Ronald R. Yager & Jana Špirková & Martin Kalina & Surajit Borkotokey, 2022. "Weight Vector Generation in Multi-Criteria Decision-Making with Basic Uncertain Information," Mathematics, MDPI, vol. 10(4), pages 1-11, February.
    4. Pollesch, N.L. & Dale, V.H., 2016. "Normalization in sustainability assessment: Methods and implications," Ecological Economics, Elsevier, vol. 130(C), pages 195-208.
    5. Gia Sirbiladze & Otar Badagadze, 2017. "Intuitionistic Fuzzy Probabilistic Aggregation Operators Based on the Choquet Integral: Application in Multicriteria Decision-Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 245-279, January.
    6. Peter Reichert & Klemens Niederberger & Peter Rey & Urs Helg & Susanne Haertel-Borer, 2019. "The need for unconventional value aggregation techniques: experiences from eliciting stakeholder preferences in environmental management," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 197-219, November.
    7. Gautam, Pooja & Shukla, Anurag, 2023. "Stochastic controllability of semilinear fractional control differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    8. Genest Christian & Scherer Matthias, 2020. "The gentleman copulist: An interview with Carlo Sempi," Dependence Modeling, De Gruyter, vol. 8(1), pages 34-44, January.
    9. Ponmana Selvan Arumugam & Won-Gil Park & Jaiok Roh, 2024. "Stability and Instability of an Apollonius-Type Functional Equation," Mathematics, MDPI, vol. 12(14), pages 1-11, July.
    10. GRABISCH, Michel & LABREUCHE, Christophe & RIDAOUI, Mustapha, 2019. "On importance indices in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 277(1), pages 269-283.
    11. Michel Grabisch & Agnieszka Rusinowska, 2010. "Iterating influence between players in a social network," Documents de travail du Centre d'Economie de la Sorbonne 10089, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    12. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    13. Vicenç Torra, 2022. "Andness Directedness for t-Norms and t-Conorms," Mathematics, MDPI, vol. 10(9), pages 1-10, May.
    14. Chunqiao Tan & Xiaohong Chen, 2016. "Generalized Archimedean Intuitionistic Fuzzy Averaging Aggregation Operators and their Application to Multicriteria Decision-Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 311-352, March.
    15. José Luis García-Lapresta & Casilda Lasso de la Vega & Ricardo Alberto Marques Pereira & Ana Marta Urrutia, 2010. "A class of poverty measures induced by the dual decomposition of aggregation functions," Working Papers 160, ECINEQ, Society for the Study of Economic Inequality.
    16. Bonifacio Llamazares, 2019. "An Analysis of Winsorized Weighted Means," Group Decision and Negotiation, Springer, vol. 28(5), pages 907-933, October.
    17. Karlson Pfannschmidt & Pritha Gupta & Bjorn Haddenhorst & Eyke Hullermeier, 2019. "Learning Context-Dependent Choice Functions," Papers 1901.10860, arXiv.org, revised Oct 2021.
    18. Radko Mesiar & Andrea Stupňanová, 2021. "Directional Shift-Stable Functions," Mathematics, MDPI, vol. 9(10), pages 1-12, May.
    19. Labreuche, Christophe & Grabisch, Michel, 2018. "Using multiple reference levels in Multi-Criteria Decision aid: The Generalized-Additive Independence model and the Choquet integral approaches," European Journal of Operational Research, Elsevier, vol. 267(2), pages 598-611.
    20. Fabrizio Durante & Juan Fernández-Sánchez & Wolfgang Trutschnig & Manuel Úbeda-Flores, 2020. "On the Size of Subclasses of Quasi-Copulas and Their Dedekind–MacNeille Completion," Mathematics, MDPI, vol. 8(12), pages 1-11, December.

    More about this item

    Keywords

    multi stability; approximation;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3458-:d:1213910. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.