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Open AccessArticle

Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

1
Department of Mathematics, Faculty of Sciences, Ibn Zohr University, Agadir 80000, Morocco
2
Institute of Mathematics, University of Zurich, CH-8057 Zurich, Switzerland
3
Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(5), 83; https://doi.org/10.3390/math6050083
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)
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
MDPI and ACS Style

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

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