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On approximation of approximate solutions of Dhombres’ equation. (English) Zbl 1133.39026

The author gives new and interesting results on the generalized Hyers-Ulam stability of Dhombres’ functional equation.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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[1] Aoki, T., On the stability of the linear transformation in Banach spaces, J. math. soc. Japan, 2, 64-66, (1950) · Zbl 0040.35501
[2] Batko, B., Stability of dhombres’ equation, Bull. austral. math. soc., 70, 499-505, (2004) · Zbl 1066.39027
[3] Bourgin, D.G., Classes of transformations and bordering transformations, Bull. amer. math. soc., 57, 223-237, (1951) · Zbl 0043.32902
[4] Dhombres, J.G., Some aspects of functional equations, (1979), Chulalongkorn University Bangkok · Zbl 0421.39005
[5] Forti, G.L., An existence and stability theorem for a class of functional equations, Stochastics, 4, 23-30, (1980) · Zbl 0442.39005
[6] Forti, G.L., Comments on the core of the direct method for proving hyers – ulam stability of functional equations, J. math. anal. appl., 295, 127-133, (2004) · Zbl 1052.39031
[7] Forti, G.L., Hyers – ulam stability of functional equations in several variables, Aequationes math., 50, 143-190, (1995) · Zbl 0836.39007
[8] Gajda, Z., On stability of additive mappings, Internat. J. math., 14, 431-434, (1991) · Zbl 0739.39013
[9] Gavruta, P., A generalization of the hyers – ulam – rassias stability of approximately additive mappings, J. math. anal. appl., 184, 431-436, (1994) · Zbl 0818.46043
[10] Ger, R., A survey of recent results on stability of functional equations, (), 5-36
[11] Ger, R., On functional inequalities stemming from stability questions, () · Zbl 0770.39007
[12] Ger, R., The singular case in the stability behaviour of linear mappings, Grazer math. ber., 316, 59-70, (1991) · Zbl 0796.39012
[13] Hyers, D.H., On the stability of the linear functional equation, Proc. natl. acad. sci. USA, 27, 222-224, (1941) · Zbl 0061.26403
[14] Hyers, D.H.; Isac, G.; Rassias, Th.M., Stability of functional equations in several variables, (1998), Birkhäuser Boston-Basel-Berlin · Zbl 0894.39012
[15] Isac, G.; Rassias, Th.M., On the hyers – ulam stability of ψ-additive mappings, J. approx. theory, 72, 131-137, (1993) · Zbl 0770.41018
[16] Jung, S., Hyers – ulam – rassias stability of functional equations in mathematical analysis, (2001), Hadronic Press Palm Harbor · Zbl 0980.39024
[17] Rassias, J.M., On approximation of approximately linear mappings by linear mappings, J. funct. anal., 46, 126-130, (1982) · Zbl 0482.47033
[18] Rassias, Th.M., On the stability of the linear mapping in Banach spaces, Proc. amer. math. soc., 72, 297-300, (1978) · Zbl 0398.47040
[19] Rassias, Th.M.; Šemrl, P., On the behavior of mappings which do not satisfy hyers – ulam stability, Proc. amer. math. soc., 114, 989-993, (1992) · Zbl 0761.47004
[20] Rassias, Th.M.; Šemrl, P., On the hyers – ulam stability of linear mappings, J. math. anal. appl., 173, 325-338, (1993) · Zbl 0789.46037
[21] Ulam, S.M., A collection of mathematical problems, (1960), Interscience New York · Zbl 0086.24101
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