Generalized Ulam-Hyers Stability of Jensen Functional Equation in Serstnev PN Spacesopen access
- Authors
- Gordji, M. Eshaghi; Ghaemi, M. B.; Majani, H.; Park, C.
- Issue Date
- Apr-2010
- Publisher
- SPRINGEROPEN
- Citation
- JOURNAL OF INEQUALITIES AND APPLICATIONS, v.2010, pp 1 - 14
- Pages
- 14
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF INEQUALITIES AND APPLICATIONS
- Volume
- 2010
- Start Page
- 1
- End Page
- 14
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/193895
- DOI
- 10.1155/2010/868193
- ISSN
- 1025-5834
1029-242X
- Abstract
- We establish a generalized Ulam-Hyers stability theorem in a Serstnev probabilistic normed space (briefly, Serstnev PN-space) endowed with Pi(M). In particular, we introduce the notion of approximate Jensen mapping in PN-spaces and prove that if an approximate Jensen mapping in a Serstnev PN-space is continuous at a point then we can approximate it by an everywhere continuous Jensen mapping. As a version of a theorem of Schwaiger, we also show that if every approximate Jensen type mapping from the natural numbers into a Serstnev PN-space can be approximated by an additive mapping, then the norm of Serstnev PN-space is complete.
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Collections - 서울 자연과학대학 > 서울 수학과 > 1. Journal Articles
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