ADDITIVE-QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN BANACH SPACES
- Authors
- Yun, Sungsik; Lee, Jung Rye; Park, Choonkil; Shin, Dong Yun
- Issue Date
- Nov-2017
- Publisher
- EUDOXUS PRESS, LLC
- Keywords
- Hyers-Ulam stability; additive-quadratic rho-functional inequality; Banach space
- Citation
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, v.23, no.7, pp.1203 - 1215
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS
- Volume
- 23
- Number
- 7
- Start Page
- 1203
- End Page
- 1215
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/151383
- ISSN
- 1521-1398
- Abstract
- Let
M(1)f(x,y): = 3/4 f(x + y) - 1/4 f(-x -y)
+1/4f(x - y) + 1/4f (y - x) - f (x) - f(y),
M(2)f(x, y) := 2f (x+ y/2) + f(x-y/2)+f(y-x/2) f(x) - f(y).
We solve the additive-quadratic rho-functional inequalities
parallel to M(1)f(x,y)parallel to <= parallel to rho M(2)f(x, y)parallel to, (0.1)
where rho is a fixed complex number with
vertical bar rho vertical bar < 1/2 and parallel to M(2)f(x,y)parallel to <= parallel to rho M(1)f(x,y)parallel to, (0.2)
where rho is a fixed complex number with vertical bar rho vertical bar < 1.
Using the direct method, we prove the Hyers-Ulam stability of the additive -quadratic rho-functional inequalities (0.1) and (0.2) in complex Banach spaces.
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