Hyers–Ulam stability of generalized Wilson’s and d’Alembert’s functional equations

Superstability problem for a large class of functional equations

“…This gives a simultaneous extension of the results in [3,[6][7][8]10,18,22,[26][27][28][29][30][31][32][33][34][35]. Therefore, our approach provide a unified treatment of the superstability of Cauchy's, d'Alembert's, Wilson's, spherical type functional equations and others.…”

“…Different generalizations of the result of Baker, Lawrence and Zorzitto was given by Badora and Ger [3,4], Székelyhidi [26,27] and Gàvruta [13]. For other superstability results, we can see for example [8,9,12,15,17,18,21,22,[30][31][32][33][34][35].…”

“…for all x, y, z ∈ G. Recently, The superstability of the functional equations on any group G and without imposing the Kannappan's conditions were investigated in [22,30,31], respectively.…”

“…The interested reader should refer to [3,4,[6][7][8][9][10][12][13][14][15][16][17][18][19][20][21][22][26][27][28][29][30][31][32][33][34][35] for a thorough account on the subject of stability of functional equations.…”

On a Composite Functional Equation Related to the Golab-Schinzel Equation

“…The first results of that kind have been studied in [3] for the exponential equation, in [2] for the cosine equation on an abelian group and in [30,31,32,33,34] for trigonmetric functional equations on any group. For further information regarding superstability of functional equations we refer to [24].…”