FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES
- Authors
- Park, Choonkil; Anastassiou, George A.; Saadati, Reza; Yun, Sungsik
- Issue Date
- Apr-2017
- Publisher
- EUDOXUS PRESS, LLC
- Keywords
- fuzzy Banach space; additive functional inequality; quadratic functional inequality; fixed point method; Hyers-Ulam stability
- Citation
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, v.22, no.4, pp.601 - 612
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
- Volume
- 22
- Number
- 4
- Start Page
- 601
- End Page
- 612
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/152585
- ISSN
- 1521-1398
- Abstract
- In this paper, we solve the following (additive functional inequality
N(f(x + y) - f(x) - f(y), t) >= N(f(x + y/2) - 1/2 f(x) - f(y), t) (0.1)
and the following quadratic functional inequality
N(f (x + y) + f (x - y) - 2f (x) - 2f (y), t) (0.2)
>= N (2f (x + y/2) + 2f (x - y/2) - f (y), t)
in fuzzy normed spaces.
Using the fixed point method, we prove the Hyers-Ulam stability of the additive functional inequality (0.1) and the quadratic functional inequality (0.2) in fuzzy Banach spaces.
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