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- W2007153184 abstract "In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982–2005 we established the Hyers–Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1998 S.-M. Jung and in 2002–2005 the authors of this paper investigated the Hyers–Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve our bounds and thus our results obtained, in 2003 for Jensen type mappings and establish new theorems about the Ulam stability of additive mappings of the second form on restricted domains. Besides we introduce alternative Jensen type functional equations and investigate pertinent stability results for these alternative equations. Finally, we apply our recent research results to the asymptotic behavior of functional equations of these alternative types. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology. En 1941 D.H. Hyers a résolu le problème bien connu de stabilité d'Ulam pour les tracés linéaires. En 1951 D.G. Bourgin était le deuxième auteur pour traiter le problème d'Ulam pour les tracés additifs. En 1982–2005 nous avons établi la stabilité de Hyers–Ulam pour le problème d'Ulam des tracés linéaires et non-linéaires. En 1998 S.-M. Jung et en 2002–2005 les auteurs de cet article ont étudié la stabilité de Hyers–Ulam des tracés additifs et quadratiques sur des domaines restreints. Dans cet article nous améliorons nos limites et ainsi nos résultats obtenus, en 2003 pour le type tracés de Jensen et établissons de nouveaux théorèmes au sujet de la stabilité d'Ulam des tracés additifs de la deuxième forme sur des domaines restreints. Sans compter que nous présentons le type alternatif équations fonctionnelles de Jensen et étudions des résultats convenables de stabilité pour ces équations alternatives. En conclusion, nous appliquons nos résultats de la recherche récents au comportement asymptotique des équations fonctionnelles de ces types alternatifs. Ces résultats de stabilité peuvent être appliqués dans l'analyse stochastique, mathématiques financières et actuarielles,aussi bien qu'en la psychologie et la sociologie." @default.
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- W2007153184 date "2005-08-01" @default.
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- W2007153184 title "Asymptotic behavior of alternative Jensen and Jensen type functional equations" @default.
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- W2007153184 doi "https://doi.org/10.1016/j.bulsci.2005.02.001" @default.
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