• 충청수학회지
• /
• 제25권1호
• /
• pp.43-49
• /
• 2012

In this paper, we investigate the stability of a functional equation $$f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)=0$$ by using the fixed point theory in the sense of L. $C\breve{a}dariu$ and V. Radu.

• 충청수학회지
• /
• 제33권1호
• /
• pp.9-18
• /
• 2020

In this paper, we investigate the stability of a quadratic-cubic-quartic functional equation $$f(x+ky)+f(x-ky)-k^2f(x+y)-k^2f(x-y)-2(1-k^2)f(x)-{\frac{k^2(k^2-1)}{6}}(f(2y)+2f(-y)-6f(y))=0$$ by applying the direct method in the sense of Gǎvruta.

• Kyungpook Mathematical Journal
• /
• 제53권2호
• /
• pp.219-232
• /
• 2013

In this paper, we investigate the stability of the functional equation $$f(x+2y)-2f(x+y)+2f(x-y)-f(x-2y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제18권4호
• /
• pp.313-328
• /
• 2011

We investigate the stability of the functional equation f(x+y+z+w)+2f(x)+2f(y)+2f(z)+2f(w)-f(x+y)-f(x+z)-f(x+w)-f(y+z)-f(y+w)-f(z+w)=0 by using a flxed point theorem in the sense of L. C$\breve{a}$adariu and V. Radu.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제17권4호
• /
• pp.363-372
• /
• 2010

In this paper we obtain the Hyers-Ulam stability of functional equations $f(x+y)=f(x)+f(y)+In\;{\alpha}^{2xy-1}$ and $f(x+y)=f(x)+f(y)+In\;{\beta(x,y)^{-1}$ which is related to the exponential and beta functions.

• 대한수학회논문집
• /
• 제25권3호
• /
• pp.405-417
• /
• 2010

We prove the generalized Hyers-Ulam stability of the generalized quadratic functional equation $$f(rx\;+\;sy)\;=\;r^2f(x)\;+\;s^2f(y)\;+\;\frac{rs}{2}[f(x\;+\;y)\;-\;f(x\;-\;y)]$$ in fuzzy Banach spaces, where r, s are non-zero rational numbers with $r^2\;+\;s^2\;{\neq}\;1$.

• 충청수학회지
• /
• 제24권4호
• /
• pp.703-712
• /
• 2011

In this paper, we investigate the stability of a cubic functional equation $$f(x+ny)+f(x-ny)+f(nx)=n^2f(x+y)+n^2f(x-y)+(n^3-2n^2+2)f(x)$$ in p-Banach spaces and in Banach modules, where $n{\geq}2$ is an integer.

• 호남수학학술지
• /
• 제41권2호
• /
• pp.391-402
• /
• 2019

In this paper, I prove the stability of the following set-valued functional equation $$f(x+2y){\oplus}f(x-2y){\oplus}3f(2x){\oplus}f(-2x)\\{\hspace{100}}=4f(x+y){\oplus}4f(x-y){\oplus}10f(x)$$ by employing the direct method in the sense of Hyers and Ulam.

• 대한수학회지
• /
• 제32권1호
• /
• pp.103-108
• /
• 1995

It is a well-known classical result of Mazur and Ulam that an isometry T from a real Banach space X onto a real Banach space Y with T(0) = 0 is automatically linear[5].

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제22권4호
• /
• pp.365-374
• /
• 2015

In this paper, we solve the additive ρ-functional equations