CUBIC AND QUARTIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY NORMED SPACES
- Authors
- Zhiang, Jooho; Chu, Jeonghun; Anastassiou, George A.; Park, Choonkil
- Issue Date
- Mar-2017
- Publisher
- EUDOXUS PRESS, LLC
- Keywords
- fuzzy Banach space; cubic rho-functional inequality; quartic rho-functional inequality; fixed point method; Hyers-Ulam stability
- Citation
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, v.22, no.3, pp.484 - 495
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
- Volume
- 22
- Number
- 3
- Start Page
- 484
- End Page
- 495
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/152746
- ISSN
- 1521-1398
- Abstract
- In this paper, we solve the following cubic rho-functional inequality
N (f(2x + y) + f(2x - y) - 2f(x + y) - 2f(x - y) - 12f(x),t) (0.1)
>= N (rho(4f(x + y/2) + 4f(x - y/2) - f(x + y) - f(x - y) - 6f(x)), t)
in fuzzy normed spaces, where rho is a fixed real number with vertical bar rho vertical bar < 2, and the following quartic rho-functional inequality
N (f(2x + y) + f(2x - y) - 4f(x + y) - 4f(x - y) - 24f(x) + 6f(y) ,t) (0.2)
>= N (rho(8f(x + y/2) + 8f(x - y/2) - 2f(x + y) - 2f(x - y) - 12f(x) + 3f(y)), t)
in fuzzy normed spaces, where rho is. a fixed real number with vertical bar rho vertical bar < 2.
Using the fixed point method, we prove the Hyers-Ulam stability of the cubic rho-functional inequality (0.1) and the quartic rho-functional inequality (0.2) in fuzzy Banach spaces.
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