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Optimum Approximation for ς –Lie Homomorphisms and Jordan ς –Lie Homomorphisms in ς –Lie Algebras by Aggregation Control Functions

Author

Listed:
  • Zahra Eidinejad

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran
    These authors contributed equally to this work.)

  • Reza Saadati

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran
    These authors contributed equally to this work.)

  • Radko Mesiar

    (Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Radlinského 11, 810 05 Bratislava, Slovakia
    Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. Listopadu 12, 771 46 Olomouc, Czech Republic
    These authors contributed equally to this work.)

Abstract

In this work, by considering a class of matrix valued fuzzy controllers and using a ( κ , ς ) -Cauchy–Jensen additive functional equation ( ( κ , ς ) -CJAFE), we apply the Radu–Mihet method (RMM), which is derived from an alternative fixed point theorem, and obtain the existence of a unique solution and the H–U–R stability (Hyers–Ulam–Rassias) for the homomorphisms and Jordan homomorphisms on Lie matrix valued fuzzy algebras with ς members ( ς -LMVFA). With regards to each theorem, we consider the aggregation function as a matrix value fuzzy control function and investigate the results obtained.

Suggested Citation

  • Zahra Eidinejad & Reza Saadati & Radko Mesiar, 2022. "Optimum Approximation for ς –Lie Homomorphisms and Jordan ς –Lie Homomorphisms in ς –Lie Algebras by Aggregation Control Functions," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1704-:d:816651
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    References listed on IDEAS

    as
    1. Soon-Mo Jung, 2011. "Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis," Springer Optimization and Its Applications, Springer, number 978-1-4419-9637-4, September.
    2. Zahra Eidinejad & Reza Saadati & Rodica Luca, 2022. "Hyers-Ulam-Rassias-Wright Stability for Fractional Oscillation Equation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-7, February.
    Full references (including those not matched with items on IDEAS)

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