Additive \(\rho\)-functional inequalities in normed spaces
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Authors
Jiyun Choi
- Mathematics Branch, Seoul Science High School, Seoul 110-530, Korea.
Juno Seong
- Mathematics Branch, Seoul Science High School, Seoul 110-530, Korea.
Choonkill Park
- Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea.
Abstract
In this paper, we solve the additive \(\rho\)-functional inequalities
\[ \| f(x + y) - f(x) - f(y)\| \leq\left\|\rho\left(2f(\frac{x+y}{2})-f(x)-f(y)\right)\right\|\quad\quad (1)\]
and
\[\left\|\left(2f(\frac{x+y}{2})-f(x)-f(y)\right)\right\|\leq \| \rho (f(x + y) - f(x) - f(y))\| \quad\quad (2)\]
where \(\rho\) is a number with \(|\rho|< 1\) . Using the fixed point method, we prove the Hyers-Ulam stability of the
additive functional inequalities (1) and (2) in normed spaces.
Share and Cite
ISRP Style
Jiyun Choi, Juno Seong, Choonkill Park, Additive \(\rho\)-functional inequalities in normed spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 1, 247--253
AMA Style
Choi Jiyun, Seong Juno, Park Choonkill, Additive \(\rho\)-functional inequalities in normed spaces. J. Nonlinear Sci. Appl. (2016); 9(1):247--253
Chicago/Turabian Style
Choi, Jiyun, Seong, Juno, Park, Choonkill. "Additive \(\rho\)-functional inequalities in normed spaces." Journal of Nonlinear Sciences and Applications, 9, no. 1 (2016): 247--253
Keywords
- Additive \(\rho\)-functional inequality
- fixed point
- Hyers-Ulam stability.
MSC
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