MMN-828

In this paper we investigate the generalized Hyers-Ulam-Rassias stability of mappings of $m-$semigroups $m \in \N; m \geq 3$ into Banach spaces. For $m=3$ the results can be found in Amyari and Moslehian [ {\it Approximately ternary semigroup homomorphisms}, Lett. Math. Phys. 77(2006), 1-9 ] with the mention that they are true in the class of normal $m-$ semigroups which is larger than the class of commutative $m-$semigroups. For $m=2$ we find certain results of Hyers [ {\it On the stability of the linear functional equation}, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224 ], Rassias, Th. M. [{\it On the stability of the linear mapping in Banach space}, Proc. Amer. Math, Soc. 72 (1978), 297-300 ] and Rassias, J. M. [ {\it Solution of a Problem of Ulam,} J. Approx. Theory Math. 57 (1989), 268-273 ]. In addition, we establish the superstability of $m-$ary homomorphims into Banach algebras endowed with multiplicative norms, generalizing the results of Szekelyhidi [ {\it On a theorem of Baker, Lawrence and Zorzitto,} Proc. Amer. Math. Soc., 84 (1982), 95-96 ] and Amyari and Moslehian (2006).

Vol. 16 (2015), No. 1, pp. 407-421

DOI: 10.18514/MMN.2015.828

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