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On the stability of mappings and an answer to a problem of Th. M. Rassias. (English) Zbl 0853.46036

Summary: The main purpose of this paper is to prove a theorem concerning the Hyers-Ulam stability of mappings, which gives a generalization of the results from [the first author, J. Math. Anal. Appl. 184, No. 3, 431-436 (1994; Zbl 0818.46043)] and [Th. M. Rassias, ibid. 158, No. 1, 106-113 (1991; Zbl 0746.46038)]. It also answers a problem posed by Th. M. Rassias [loc. cit.].

MSC:

46G05 Derivatives of functions in infinite-dimensional spaces
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References:

[1] Găvruţa, P., A generalization of the HYERS-ULAM-RASSIAS stability of approximately additive mappings ,Journal of Math. Analysis and Appl.184 (1994), 431-436. · Zbl 0818.46043
[2] Hyers, D.H.AND Rassias, Th.M., Approximate homomorphisms , Aequationes Math.44 (1992), 125-153. · Zbl 0806.47056
[3] Rassias, Th.M., On a modified HYERS-ULAM sequence , Journal of Math. Analysis and Appl.158 (1991), 106-113. · Zbl 0746.46038
[4] Ulam, S.M., Problems in modern mathematics, chap. VI, Science eds. ,Wiley, New York, 1960. · Zbl 0137.24201
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