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2013 | 11 | 5 | 966-971
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Some remarks on the stability of the multi-Jensen equation

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EN
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EN
First a stability result of Prager-Schwaiger [Prager W., Schwaiger J., Stability of the multi-Jensen equation, Bull. Korean Math. Soc., 2008, 45(1), 133–142] is generalized by admitting more general domains of the involved function and by allowing the bound to be not constant. Next a result by Cieplinski [Cieplinski K., On multi-Jensen functions and Jensen difference, Bull. Korean Math. Soc., 2008, 45(4), 729–737] is discussed. Finally a characterization of the completeness of a normed space in terms of stability requirements for multi-Jensen functions is presented.
Słowa kluczowe
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Tom
11
Numer
5
Strony
966-971
Opis fizyczny
Daty
wydano
2013-05-01
online
2013-03-14
Twórcy
Bibliografia
  • [1] Brzdek J., The Cauchy and Jensen differences on semigroups, Publ. Math. Debrecen, 1996, 48(1–2), 117–136
  • [2] Bae J.-H., Park W.-G., On the solution of a bi-Jensen functional equation and its stability, Bull. Korean Math. Soc., 2006, 43(3), 499–507 http://dx.doi.org/10.4134/BKMS.2006.43.3.499
  • [3] Cieplinski K., On multi-Jensen functions and Jensen difference, Bull. Korean Math. Soc., 2008, 45(4), 729–737 http://dx.doi.org/10.4134/BKMS.2008.45.4.729
  • [4] Cieplinski K., Stability of the multi-Jensen equation, J. Math. Anal. Appl., 2010, 363(1), 249–254 http://dx.doi.org/10.1016/j.jmaa.2009.08.021
  • [5] Forti G.L., Hyers-Ulam stability of functional equations in several variables, Aequationes Math., 1995, 50(1–2), 143–190 http://dx.doi.org/10.1007/BF01831117
  • [6] Forti G.L., Schwaiger J., Stability of homomorphisms and completeness, C. R. Math. Rep. Acad. Sci. Canada, 1989, 11(6), 215–220
  • [7] Jung S.-M., Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer Optim. Appl., 48, Springer, New York, 2011
  • [8] Prager W., Schwaiger J., Multi-affine and multi-Jensen functions and their connection with generalized polynomials, Aequationes Math., 2005, 69(1–2), 41–57 http://dx.doi.org/10.1007/s00010-004-2756-4
  • [9] Prager W., Schwaiger J., Stability of the multi-Jensen equation, Bull. Korean Math. Soc., 2008, 45(1), 133–142 http://dx.doi.org/10.4134/BKMS.2008.45.1.133
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0215-y
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