Bulletin of the
Korean Mathematical Society
BKMS
Article
ALL ARTICLES
View
Bull. Korean Math. Soc. 2009; 46(2): 387-400
Printed March 1, 2009
https://doi.org/10.4134/BKMS.2009.46.2.387
Copyright © The Korean Mathematical Society.
Approximately additive mappings in non-Archimedean normed spaces
Alireza Kamel Mirmostafaee
Ferdowsi University of Mashhad
We establish a new strategy to study the Hyers-Ulam-Rassias stability of the Cauchy and Jensen equations in non-Archimedean normed spaces. We will also show that under some restrictions, every function which satisfies certain inequalities can be approximated by an additive mapping in non-Archimedean normed spaces. Some applications of our results will be exhibited. In particular, we will see that some results about stability and additive mappings in real normed spaces are not valid in non-Archimedean normed spaces.
Keywords: Hyers-Ulam-Rassias stability, Cauchy equation, Jensen equation, Jordan-von Neumann-type Jensen inequality
MSC numbers: Primary 39B82, 39B22, 46S10; Secondary 39B62
Article Tools
Stats or Metrics
Share this article on :
Related articles in BKMS
-
Substitution operators in the spaces of functions of bounded variation $BV_\alpha^2(I)$
2015; 52(2): 649-659
-
Uniformly bounded composition operators on a Banach space of bounded Wiener-Young variation functions
2013; 50(2): 675-685
-
On the Hyers-Ulam-Rassias stability of the equation $f(x^2-y^2+rxy)=f(x^2)-f(y^2)+rf(xy)$
1996; 33(4): 513-519
-
On the generalized Hyers-Ulam-Rassias stability of a quadratic functional equation
2001; 38(2): 325-336
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd