On the Ulam stability of Jensen and Jensen type mappings on restricted domains
By John Michael Rassias, Matina John Rassias. 2003
87 citations recorded by the source corpus.
In 1941 Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 Bourgin was the second author to treat this problem for additive mappings. In 1982–1998 Rassias established the Hyers–Ulam stability of linear and nonlinear mappings. In 1983 Skof was the first author to solve the same problem on a restricted domain. In 1998 Jung investigated the Hyers–Ulam stability of more general mappings on restricted domains. In this paper we introduce additive mappings of two forms: of “Jensen” and “Jensen type,” and achieve the Ulam stability of these mappings on restricted domains. Finally, we apply our results to the asymptotic behavior of the functional equations of these types.
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/ff987699161f83241b21dfe556482630c10aa84c
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In Algebra and Number Theory
In Applied Mathematics
- Hark-Mahn Kim
- Gian Luigi Forti
- John Michael Rassias
- Matina John Rassias
- K. Jun
- Janusz Brzdek
- M. Eshaghi Gordji
- Abbas Najati
Citations in the corpus
- Hyperstability of the Jensen functional equation (2014, unknown): “, [3,5–8,10]).”
- Elementary remarks on Ulam–Hyers stability of linear functional equations (2007, background): “Many of them treat functional equations in several variables and what is given is an inequality in several variables and the first step in order to prove stability consists in certain manipulations transforming that inequality in several variables in an inequality in one variable (see, for instance,”
- Asymptotic behavior of alternative Jensen and Jensen type functional equations (2005, methodology): “Rassias [16– 21,23,24] and in 2003 and 2005 the authors [22,25] solved the above Ulam problem for Jensen and Euler–Lagrange type mappings.”
- Extended Hyers–Ulam stability for Cauchy–Jensen mappings (2007, background): “Rassias [25,26] and Rassias[27] solved the above Ulam problem for Jensen and Jensen type mappings.”
- Generalized Hyers–Ulam stability for general additive functional equations in quasi-β-normed spaces☆ (2009, background): “1) yields Jensen additive equation 2g( x+y 2 ) = g(x) + g(y) and there are many interesting results concerning the stability problems of the Jensen equation [10,14,16].”