Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

Elhoucien Elqorachi and Michael Th. Rassias
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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

Mathematics, 2018, vol. 6, issue 5, 1-11

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 .

Keywords: Hyers-Ulam stability; trigonometric functional equations; semigroup (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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