CUBIC AND QUARTIC ρ-FUNCTIONAL INEQUALITIES IN FUZZY BANACH SPACESopen access
- Authors
- Park, Choonkil
- Issue Date
- Dec-2016
- Publisher
- ELEMENT
- Keywords
- Fuzzy Banach space; cubic rho-functional inequality; quartic rho-functional inequality; fixed point method; Hyers-Ulam stability
- Citation
- JOURNAL OF MATHEMATICAL INEQUALITIES, v.10, no.4, pp.1123 - 1136
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF MATHEMATICAL INEQUALITIES
- Volume
- 10
- Number
- 4
- Start Page
- 1123
- End Page
- 1136
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/153455
- DOI
- 10.7153/jmi-10-89
- ISSN
- 1846-579X
- 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) (0.1)
-rho(4f(x + y/2) + 4f(x - y/2) - f(x + y) - f(x - y) - 6f(x)),t) >= t/t + phi(x, y)
and the following quartic rho-functional inequality
N(f(2x + y) + f(2x - y) - 4f(x + y) - 4f(x - y) - 24f(x) + 6f(y) (0.2)
-rho(8f(x + y/2) + 8f(x - y/2) - 2f(x + y) - 2f(x - y) - 12f(x) + 3f(y)),t)
>= t/t + phi(x, y)
in fuzzy normed spaces, where. is a fixed real number with rho not equal 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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