ON THE SUPERSTABILITY OF THE PEXIDER TYPE GENERALIZED TRIGONOMETRIC FUNCTIONAL EQUATIONS

doi:10.1016/S0252-9602(14)60120-X

Abstract

Abstract:

The aim of this paper is to investigate the superstability problem for the pex-iderized trigonometric functional equation
∑_φ∈Φ∫_Kf(xkφ(y)k⁻¹)dwK(k) =|Φ|g(x)h(y), x, y ∈ G,
where G is any topological group, K is a compact subgroup of G, !K is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions. Consequently, we have generalized the results of stability for d’Alembert´s and Wilson´s equa-tions by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H. Kim, J.M. Rassias, A. Roukbi, L. Sz´ekelyhidi, D. Zeglami, etc.

Key words: superstability, generalized Pexider d´Alembert equation, Wilson´s functional equation, group of morphisms

CLC Number:

39B72

Driss ZEGLAMI, Ahmed CHARIFI, Samir KABBAJ. ON THE SUPERSTABILITY OF THE PEXIDER TYPE GENERALIZED TRIGONOMETRIC FUNCTIONAL EQUATIONS[J].Acta mathematica scientia,Series B, 2014, 34(6): 1749-1760.

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