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Mathematics 2018, 6(5), 83;

Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

Department of Mathematics, Faculty of Sciences, Ibn Zohr University, Agadir 80000, Morocco
Institute of Mathematics, University of Zurich, CH-8057 Zurich, Switzerland
Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
Author to whom correspondence should be addressed.
Received: 18 April 2018 / Revised: 2 May 2018 / Accepted: 11 May 2018 / Published: 18 May 2018
(This article belongs to the Special Issue Stability Problems)
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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. View Full-Text
Keywords: Hyers-Ulam stability; trigonometric functional equations; semigroup Hyers-Ulam stability; trigonometric functional equations; semigroup
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Elqorachi, E.; Rassias, M.T. Generalized Hyers-Ulam Stability of Trigonometric Functional Equations. Mathematics 2018, 6, 83.

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