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Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

Author

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  • Elhoucien Elqorachi

    (Department of Mathematics, Faculty of Sciences, Ibn Zohr University, Agadir 80000, Morocco)

  • Michael Th. Rassias

    (Institute of Mathematics, University of Zurich, CH-8057 Zurich, Switzerland
    Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia)

Abstract

In the present paper we study the generalized Hyers–Ulam stability of the generalized trigonometric functional equations f ( x y ) + μ ( y ) f ( x σ ( y ) ) = 2 f ( x ) g ( y ) + 2 h ( y ) , x , y ∈ S ; f ( x y ) + μ ( y ) f ( x σ ( y ) ) = 2 f ( y ) g ( x ) + 2 h ( x ) , x , y ∈ S , where S is a semigroup, σ : S ⟶ S is a involutive morphism, and μ : S ⟶ C is a multiplicative function such that μ ( x σ ( x ) ) = 1 for all x ∈ S . As an application, we establish the generalized Hyers–Ulam stability theorem on amenable monoids and when σ is an involutive automorphism of S .

Suggested Citation

  • Elhoucien Elqorachi & Michael Th. Rassias, 2018. "Generalized Hyers-Ulam Stability of Trigonometric Functional Equations," Mathematics, MDPI, vol. 6(5), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:5:p:83-:d:147588
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    References listed on IDEAS

    as
    1. Soon-Mo Jung & Dorian Popa & Michael Rassias, 2014. "On the stability of the linear functional equation in a single variable on complete metric groups," Journal of Global Optimization, Springer, vol. 59(1), pages 165-171, May.
    2. Zbigniew Gajda, 1991. "On stability of additive mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, January.
    3. Roman Badora, 2011. "Stability Properties of Some Functional Equations," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 3-13, Springer.
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    Cited by:

    1. Janusz Brzdęk & El-sayed El-hady, 2020. "On Hyperstability of the Cauchy Functional Equation in n -Banach Spaces," Mathematics, MDPI, vol. 8(11), pages 1-12, October.

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