The Superstability of the Generalized D'alembert Functional Equation

Elqorachi, Elhoucien; Akkouchi, Mohamed

doi:10.1515/gmj.2003.503

Cited by 16 publications

(7 citation statements)

References 3 publications

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“…It involves an interesting generalization of the class of bounded function on a group or semigroup. For other stability and superstability results, we can see for example [2], [3], [4], [7], [14], [19], [20] and [36], the present authors [6] for general groups. Various stability results of Wilson's functional equation and it's generalization are obtained.…”

supporting

confidence: 51%

Solutions and stability of variant of Wilson's functional equation

Elqorachi¹,

Redouani²

2015

Preprint

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In this paper we will investigate the solutions and stability of the generalized variant of Wilson's functional equationwhere G is a group, σ is an involutive morphism of G and χ is a character of G. (a) We solve (E) when σ is an involutive automorphism, and we obtain some properties about solutions of (E) when σ is an involutive anti-automorphism. (b) We obtain the Hyers Ulam stability of equation (E). As an application, we prove the superstability of the functional equation f (xy) + χ(y)f (σ(y)x) = 2f (x)f (y), x, y ∈ G. 2, where φ is multiplicative. There has been quite a development of the theory of d'Alembert's functional equation (1.1) during the last years, on non abelian groups, as shown in works by Dilian yang about compact groups [10,11,12], Stetkaer [42] for step 2 nilpotent groups, Friis [17] for results on Lie groups and Davison [8,9]

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supporting

confidence: 51%

Solutions and stability of variant of Wilson's functional equation

Elqorachi¹,

Redouani²

2015

Preprint

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“…Then, i) f, g are bounded or ii) f is unbounded and g satisfies the functional equation The following corollary is a generalization of the result obtained by E. Elqorachi and M. Akkouchi in [17] under the condition that f satisfies the Kannappan type condition or µ is a generalized Gelfand measure.…”

Section: Now By Using (22) and (23) We Obtainmentioning

confidence: 63%

“…It involves an interesting generalization of the class of bounded function on a group or semigroup. For other superstability results, we can see for example [17], [12], [23], [31], [32] and [48].…”

mentioning

confidence: 86%

Hyers–Ulam stability of spherical functions

Bouikhalene

Elhoucien

2016

Georgian Mathematical Journal

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“…Different generalization of the result of Baker, Lawrence and Zorzitto have been obtained. We mention for example [4], [14], [19], [21], [22], [24], [25] and [28].…”

Section: Introductionmentioning

confidence: 99%

Solutions and stability of generalized Kannappan's and Van Vleck's functional equations

Elqorachi¹,

Redouani²

2016

Preprint

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We study the solutions of the integral Kannappan's and Van Vleck's functional equationswhere S is a semigroup, σ is an involutive automorphism of S and µ is a linear combination of Dirac measures (δz i ) i∈I , such that for all i ∈ I, z i is contained in the center of S. We show that the solutions of these equations are closely related to the solutions of the d'Alembert's classic functional equation with an involutive automorphism. Furthermore, we obtain the superstability theorems that these functional equations are superstable in the general case, where σ is an involutive morphism.

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The Superstability of the Generalized D'alembert Functional Equation

Cited by 16 publications

References 3 publications

Solutions and stability of variant of Wilson's functional equation

Solutions and stability of variant of Wilson's functional equation

Hyers–Ulam stability of spherical functions

Solutions and stability of generalized Kannappan's and Van Vleck's functional equations

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