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APPROXIMATELY ADDITIVE MAPPINGS IN NON-ARCHIMEDEAN NORMED SPACES
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 Title & Authors
APPROXIMATELY ADDITIVE MAPPINGS IN NON-ARCHIMEDEAN NORMED SPACES
Mirmostafaee, Alireza Kamel;
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 Abstract
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;
 Language
English
 Cited by
1.
Hyers-Ulam Stability of Cubic Mappings in Non-Archimedean Normed Spaces,;

Kyungpook mathematical journal, 2010. vol.50. 2, pp.315-327 crossref(new window)
2.
Approximately Orthogonal Additive Set-valued Mappings,;;

Kyungpook mathematical journal, 2013. vol.53. 4, pp.639-646 crossref(new window)
1.
Stability of a general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces, Journal of Mathematical Physics, 2010, 51, 9, 093508  crossref(new windwow)
2.
Stability of a Quartic Functional Equation, The Scientific World Journal, 2014, 2014, 1  crossref(new windwow)
3.
Stability of then-Dimensional Mixed-Type Additive and Quadratic Functional Equation in Non-Archimedean Normed Spaces, Abstract and Applied Analysis, 2012, 2012, 1  crossref(new windwow)
4.
Approximately Orthogonal Additive Set-valued Mappings, Kyungpook mathematical journal, 2013, 53, 4, 639  crossref(new windwow)
5.
Stability of mixed additive–quadratic Jensen type functional equation in various spaces, Computers & Mathematics with Applications, 2011, 61, 9, 2704  crossref(new windwow)
6.
Hyers-Ulam Stability of Cubic Mappings in Non-Archimedean Normed Spaces, Kyungpook mathematical journal, 2010, 50, 2, 315  crossref(new windwow)
7.
A Fixed Point Approach to the Stability of a General Mixed AQCQ-Functional Equation in Non-Archimedean Normed Spaces, Discrete Dynamics in Nature and Society, 2010, 2010, 1  crossref(new windwow)
8.
Nonlinear approximation of an ACQ-functional equation in nan-spaces, Fixed Point Theory and Applications, 2011, 2011, 1, 60  crossref(new windwow)
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