Stability of Wilson’s functional equations with involutions

Chung, Jaeyoung; Sahoo, Prasanna K.

doi:10.1007/s00010-014-0262-x

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…Recently, Ebanks, Stetkaer [13] and Stetkaer [28] [2], [3], [6], [9], [15], [16], [17], [20], [21], [22], [23], [24], [25], [29] and [32], for a thorough account on the subject of stability of functional equations. The aim of this paper is to study some properties of the solutions and Hyers-Ulam stability of some generalization of d'Alembert's and Wilson's functional equations which has been introduced in [14].…”

Section: Introductionmentioning

confidence: 99%

“…On abelian groups, the stability of d'Alembert's functional equation (1.2) and Wilson's functional equation (1.4) and other functional equation has been investigated by several authors. The interested reader should refer to [2], [3], [6], [9], [15], [16], [17], [20], [21], [22], [23], [24], [25], [29] and [32], for a thorough account on the subject of stability of functional equations. The aim of this paper is to study some properties of the solutions and Hyers-Ulam stability of some generalization of d'Alembert's and Wilson's functional equations which has been introduced in [14].…”

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confidence: 99%

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Solutions and stability of a generalization of wilson's equation

Bouikhalene

Elqorachi

2016

Acta Mathematica Scientia

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Abstract. In this paper we study the solutions and stability of the generalized Wilson's functional equation G f (xty)dµ(t)+ G f (xtσ(y))dµ(t) = 2f (x)g(y), x, y ∈ G, where G is a locally compact group, σ is a continuous involution of G and µ is an idempotent complex measure with compact support and which is σ-invariant. We show that G g(xty)dµ(t) + G g(xtσ(y))dµ(t) = 2g(x)g(y), x, y ∈ G if f = 0 and G f (t.)dµ(t) = 0. We also study some stability theorems of that equation and we establish the stability on noncommutaive groups of the classical Wilson's functional equation f (xy) + χ(y)f (xσ(y)) = 2f (x)g(y) x, y ∈ G , where χ is a unitary character of G.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Solutions and stability of a generalization of wilson's equation

Bouikhalene

Elqorachi

2016

Acta Mathematica Scientia

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“…The interested reader should refer to [3,4,7,9,21,[25][26][27]40,41], for a thorough account on the subject of stability of functional equations.…”

Section: Introductionmentioning

confidence: 99%

Stability of a generalization of Wilson’s equation

Bouikhalene

Elqorachi

2015

Aequat. Math.

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Given a character μ: G → C \ {0} and an involution σ of a group G we study the solutions f, g: G −→ C of the functional equationfrom the theory of trigonometric functional equations. (1) We show that g satisfies g(xy) + μ(y)g(xσ(y)) = 2g(x)g(y) if f = 0. (2) We derive hyperstability results for the equation, when μ is unitary. This generalizes the classic case, in which μ = 1 and σ is the group inversion.Mathematics Subject Classification. 39B82, 39B32, 39B52.

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