Stability of Functional Equations and Properties of Groups

[1] R. Badora, On the Hahn–Banach theorem for groups, Arch. Math. (Basel) 86 (2006), no. 6, 517–528.10.1007/s00013-005-1570-0Search in Google Scholar

[2] R. Badora, B. Przebieracz, P. Volkmann, On Tabor groupoids and stability of some functional equations, Aequationes Math. 87 (2014), no. 1–2, 165–171.10.1007/s00010-013-0206-xSearch in Google Scholar

[3] A. Bahyrycz, Forti’s example of an unstable homomorphism equation, Aequationes Math. 74 (2007), no. 3, 310–313.10.1007/s00010-007-2882-xSearch in Google Scholar

[4] J. Dixmier, Les moyennes invariantes dans les semi-groups et leurs applications, Acta. Sci. Math. Szeged 12 (1950), 213–227.Search in Google Scholar

[5] G.-L. Forti, The stability of homomorphisms and amenability, with applications to functional equations, Abh. Math. Sem. Univ. Hamburg 57 (1987), 215–226.10.1007/BF02941612Search in Google Scholar

[6] G.-L. Forti, Hyers–Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1–2, 143–190.10.1007/BF01831117Search in Google Scholar

[7] G.-L. Forti, J. Sikorska, Variations on the Drygas equation and its stability, Nonlinear Anal. 74 (2011), no. 2, 343–350.10.1016/j.na.2010.08.004Search in Google Scholar

[8] Z. Gajda, Z. Kominek, On separation theorems for subadditive and superadditive functionals, Studia Math. 100 (1991), no. 1, 25–38.10.4064/sm-100-1-25-38Search in Google Scholar

[9] F.P. Greenleaf, Invariant Means on Topological Groups, Van Nostrand Mathematical Studies 16, Van Nostrand Reinhold Co., New York–Toronto–London–Melbourne, 1969.Search in Google Scholar

[10] D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222–224.10.1073/pnas.27.4.222107831016578012Search in Google Scholar

[11] S.V. Ivanov, The free Burnside groups of sufficiently large exponents, Internat. J. Algebra Comput. 4 (1994), no. 1–2, 1–308.10.1142/S0218196794000026Search in Google Scholar

[12] W. Magnus, A. Karrass, D. Solitar, Combinatorial Group Theory, Dover Publications, Inc., New York, 1976.Search in Google Scholar

[13] P.S. Novikov, S.I. Adian, Infinite periodic groups. I–III. (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 212–244, 251–254, 709–731.Search in Google Scholar

[14] A.Yu. Ol’shanskii, On the question of the existence of an invariant mean on a group. (Russian), Uspekhi Mat. Nauk 35 (1980), no. 4(214), 199–200.10.1070/RM1980v035n04ABEH001876Search in Google Scholar

[15] A.Yu. Ol’shanskii, The Novikov–Adian theorem. (Russian), Mat. Sb. (N.S.) 118(160) (1982), no. 2, 203–235.10.1070/SM1983v046n02ABEH002768Search in Google Scholar

[16] D.V. Osin, Uniform non-amenability of free Burnside groups, Arch. Math. (Basel) 88 (2007), no. 5, 403–412.10.1007/s00013-006-2002-5Search in Google Scholar

[17] J. Rätz, On approximately additive mappings, in: E.F. Beckenbach (ed.), General Inequalities. 2, Proc. Second Internat. Conf., Oberwolfach 1978, Birkhäuser, Basel, 1980, pp. 233–251.10.1007/978-3-0348-6324-7_22Search in Google Scholar

[18] E. Shulman, Group representations and stability of functional equations, J. London Math. Soc. (2) 54 (1996), no. 1, 111–120.10.1112/jlms/54.1.111Search in Google Scholar

[19] E. Shulman, Addition theorems and related geometric problems of group representation theory, in: J. Brzd¦k et al. (eds.), Recent Developments in Functional Equations and Inequalities, Banach Center Publ., vol. 99, Polish Acad. Sci. Inst. Math., Warsaw, 2013, pp. 155–172.10.4064/bc99-0-10Search in Google Scholar

[20] F. Skof, Proprietà locali e approssimazione di operatori. Geometry of Banach spaces and related topics (Milan, 1983), Rend. Sem. Mat. Fis. Milano 53 (1983), 113–129 (1986).10.1007/BF02924890Search in Google Scholar

[21] L. Székelyhidi, Note on a stability theorem, Canad. Math. Bull. 25 (1982), no. 4, 500–501.10.4153/CMB-1982-074-0Open DOISearch in Google Scholar

[22] L. Székelyhidi, Remark 17, 22sd International Symposium on Functional Equations, Oberwolfach 1984, Aequationes Math. 29 (1985), no. 1, 95.Search in Google Scholar

[23] J. Tabor, Remark 18, 22sd International Symposium on Functional Equations, Oberwolfach 1984, Aequationes Math. 29 (1985), no. 1, 96.Search in Google Scholar

[24] I. Toborg, Tabor groups with finiteness conditions, Aequationes Math. 90 (2016), no. 4, 699–704.10.1007/s00010-015-0369-8Search in Google Scholar

[25] D. Yang, Remarks on the stability of Drygas’ equation and the Pexider–quadratic equation, Aequationes Math. 68 (2004), no. 1–2, 108–116.10.1007/s00209-003-0573-4Open DOISearch in Google Scholar

[26] D. Yang, The stability of the quadratic functional equation on amenable groups, J. Math. Anal. Appl. 291 (2004), no. 2, 666–672.10.1016/j.jmaa.2003.11.021Search in Google Scholar