[[1] Badora R., On a joint generalization of Cauchy’s and d’Alembert’s functional equations, Aequationes Math. 43 (1992), no. 1, 72-89.]Search in Google Scholar
[[2] Baker J.A., The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), 411-416.10.1090/S0002-9939-1980-0580995-3]Open DOISearch in Google Scholar
[[3] Baker J.A., Lawrence J., Zorzitto F., The stability of the equation f(x+y) = f(x)f(y), Proc. Amer. Math. Soc. 74 (1979), 242-246.]Search in Google Scholar
[[4] Bouikhalene B., Elqorachi E., An extension of Van Vleck’s functional equation for the sine, Acta Math. Hungar. 150 (2016), no. 1, 258-267.]Search in Google Scholar
[[5] Bouikhalene B., Elqorachi E., Rassias J.M., The superstability of d’Alembert’s functional equation on the Heisenberg group, Appl. Math. Lett. 23 (2000), no. 1, 105-109.]Search in Google Scholar
[[6] Bouikhalene B., Elqorachi E., Hyers-Ulam stability of spherical function, Georgian Math. J. 23 (2016), no. 2, 181-189.]Search in Google Scholar
[[7] d’Alembert J., Recherches sur la courbe que forme une corde tendue mise en vibration, I, Hist. Acad. Berlin 1747 (1747), 214-219.]Search in Google Scholar
[[8] d’Alembert J., Recherches sur la courbe que forme une corde tendue mise en vibration, II, Hist. Acad. Berlin 1747 (1747), 220-249.]Search in Google Scholar
[[9] d’Alembert J., Addition au Mémoire sur la courbe que forme une corde tendue mise en vibration, Hist. Acad. Berlin 1750 (1750), 355-360.]Search in Google Scholar
[[10] Davison T.M.K., D’Alembert’s functional equation on topological groups, Aequationes Math. 76 (2008), no. 1-2, 33-53.]Search in Google Scholar
[[11] Davison T.M.K., D’Alembert’s functional equation on topological monoids, Publ. Math. Debrecen 75 (2009), no. 1-2, 41-66.]Search in Google Scholar
[[12] Ebanks B.R., Stetkær H., d’Alembert’s other functional equation on monoids with an involution, Aequationes Math. 89 (2015), no. 1, 187-206.]Search in Google Scholar
[[13] Elqorachi E., Integral Van Vleck’s and Kannappan’s functional equations on semigroups, Aequationes Math. 91 (2017), no. 1, 83-98.]Search in Google Scholar
[[14] Elqorachi E., Akkouchi M., The superstability of the generalized d’Alembert functional equation, Georgian Math. J. 10 (2003), no. 3, 503-508.]Search in Google Scholar
[[15] Elqorachi E., Akkouchi M., On generalized d’Alembert and Wilson functional equations, Aequationes Math. 66 (2003), no. 3, 241-256.]Search in Google Scholar
[[16] Elqorachi E., Akkouchi M., Bakali A., Bouikhalene B., Badora’s equation on nonabelian locally compact groups, Georgian Math. J. 11 (2004), no. 3, 449-466.]Search in Google Scholar
[[17] Elqorachi E., Bouikhalene B., Functional equation and µ-spherical functions, Georgian Math. J. 15 (2008), no. 1, 1-20.]Search in Google Scholar
[[18] Elqorachi E., Redouani A., Rassias Th.M., Solutions and stability of a variant of Van Vleck’s and d’Alembert’s functional equations, Int. J. Nonlinear Anal. Appl. 7 (2016), no. 2, 279-301.]Search in Google Scholar
[[19] Ger R., Superstability is not natural, Rocznik Nauk.-Dydakt. Prace Mat. 159 (1993), no. 13, 109-123.]Search in Google Scholar
[[20] Ger R., Šemrl P., The stability of the exponential equation, Proc. Amer. Math. Soc. 124 (1996), no. 3, 779-787.]Search in Google Scholar
[[21] Forti G.L., Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143-190.]Search in Google Scholar
[[22] Hyers D.H., Isac G.I., Rassias Th.M., Stability of Functional Equations in Several Variables, Birkhäuser, Basel, 1998.10.1007/978-1-4612-1790-9]Search in Google Scholar
[[23] Kannappan Pl., A functional equation for the cosine, Canad. Math. Bull. 2 (1968), 495-498.10.4153/CMB-1968-059-8]Open DOISearch in Google Scholar
[[24] Kim G.H, On the stability of trigonometric functional equations, Adv. Difference Equ. 2007, Article ID 90405, 10 pp.10.1155/2007/90405]Search in Google Scholar
[[25] Kim G.H., On the stability of the Pexiderized trigonometric functional equation, Appl. Math. Comput. 203 (2008), no. 1, 99-105.]Search in Google Scholar
[[26] Lawrence J., The stability of multiplicative semigroup homomorphisms to real normed algebras, Aequationes Math. 28 (1985), no. 1-2, 94-101.]Search in Google Scholar
[[27] Perkins A.M., Sahoo P.K., On two functional equations with involution on groups related to sine and cosine functions, Aequationes Math. 89 (2015), no. 5, 1251-1263.]Search in Google Scholar
[[28] Redouani A., Elqorachi E., Rassias M.Th., The superstability of d’Alembert’s functional equation on step 2 nilpotent groups, Aequationes Math. 74 (2007), no. 3, 226-241.]Search in Google Scholar
[[29] Sinopoulos P., Contribution to the study of two functional equations, Aequationes Math. 56 (1998), no. 1-2, 91-97.]Search in Google Scholar
[[30] Stetkær H., d’Alembert’s equation and spherical functions, Aequationes Math. 48 (1994), no. 2-3, 220-227.]Search in Google Scholar
[[31] Stetkær H., Functional Equations on Groups, World Scientific Publishing Co, Singapore, 2013.10.1142/8830]Search in Google Scholar
[[32] Stetkær H., A variant of d’Alembert’s functional equation, Aequationes Math. 89 (2015), no. 3, 657-662.]Search in Google Scholar
[[33] Stetkær H., Van Vleck’s functional equation for the sine, Aequationes Math. 90 (2016), no. 1, 25-34.]Search in Google Scholar
[[34] Stetkær H., Kannappan’s functional equation on semigroups with involution, Semigroup Forum 94 (2017), 17-33.10.1007/s00233-015-9756-7]Open DOISearch in Google Scholar
[[35] Van Vleck E.B., A functional equation for the sine, Ann. of Math. (2) 11 (1910), no. 4, 161-165.10.2307/1967133]Open DOISearch in Google Scholar
[[36] Van Vleck E.B., On the functional equation for the sine. Additional note on: “A functional equation for the sine”, Ann. of Math. (2) 13 (1911/12), no. 1-4, 154.10.2307/1968082]Search in Google Scholar