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Mathematics 2018, 6(5), 83; https://doi.org/10.3390/math6050083

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.
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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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. 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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