• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.161-170
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• 2018

In this paper, we introduce and solve the following additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) $${\parallel}f(x+y+z)-f(x)-f(y)-f(z){\parallel}{\leq}{\parallel}{\rho}_1(f(x+z)-f(x)-f(z)){\parallel}+{\parallel}{\rho}_2(f(y+z)-f(y)-f(z)){\parallel}$$, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with ${\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}$ < 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) in complex Banach spaces.

• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.21-31
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• 2017

In this paper, we introduce and solve the following additive (${\rho}_1$, ${\rho}_2$)-functional inequality $${\Large{\parallel}}2f(\frac{x+y}{2})-f(x)-f(y){\Large{\parallel}}{\leq}{\parallel}{\rho}_1(f(x+y)+f(x-y)-2f(x)){\parallel}+{\parallel}{\rho}_2(f(x+y)-f(x)-f(y)){\parallel}$$ where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with $\sqrt{2}{\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}<1$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1$, ${\rho}_2$)-functional inequality (1) in complex Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.197-211
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• 2013

We study some stability properties in discrete Volterra equations by employing to change Yoshizawa's results in [13] for the nonlinear equations into results for the nonlinear discrete Volterra equations with unbounded delay.

• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.219-227
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• 2018

In this paper, we solve the additive ${\rho}$-functional equations $$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < 1, and $$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ${\rho}$-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.179-190
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• 2017

In this paper, we introduce and solve the following quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) $$N\left(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y),t\right){\leq}min\left(N({\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y)),t),\;N({\rho}_2(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)),t)\right)$$ in fuzzy normed spaces, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero real numbers with ${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$ < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) in fuzzy Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.753-762
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• 2012

We study the BS-stability and the $\rho$-stability for functional difference equations with infinite delay as a discretization of Murakami and Yoshizawa's results [6] for functional differential equation with infinite delay.

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.109-127
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• 2017

In this paper, we solve the following quadratic ${\rho}-functional$ inequalities ${\parallel}f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z){\parallel}$ (0.1) ${\leq}{\parallel}{\rho}(f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\frac{1}{{\mid}4{\mid}}}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}$ (0.2) ${\leq}{\parallel}{\rho}(f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\mid}8{\mid}$. Using the direct method, we prove the Hyers-Ulam stability of the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of quadratic ${\rho}-functional$ equations associated with the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.317-323
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• 2014

In this paper, we solve the additive functional inequality $${\parallel}f(x)+f(y)+f(z){\parallel}{\leq}{\parallel}{\rho}f(s(x+y+z)){\parallel}$$, where s is a nonzero real number and ${\rho}$ is a real number with ${\mid}{\rho}{\mid}$ < 3. Moreover, we prove the Hyers-Ulam stability of the above additive functional inequality in Banach spaces.

• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.243-251
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• 2017

In this paper, we solve the additive ${\rho}-functional$ equations (0.1) $f(x+y)+f(x-y)-2f(x)={\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x))$, and (0.2) $2f(\frac{x+y}{2})+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$, where ${\rho}$ is a fixed (complex) number with ${\rho}{\neq}1$, Using the direct method, we prove the Hyers-Ulam stability of the additive ${\rho}-functional$ equations (0.1) and (0.2) in ${\beta}-homogeneous$ (complex) F-spaces.

• Journal of Microbiology and Biotechnology
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• v.30 no.10
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• pp.1488-1494
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• 2020

Rho guanine nucleotide dissociation inhibitor 1 (RhoGDI1) plays important roles in numerous cellular processes, including cell motility, adhesion, and proliferation, by regulating the activity of Rho GTPases. Its expression is altered in various human cancers and is associated with malignant progression. Here, we show that RhoGDI1 interacts with Cullin 3 (CUL3), a scaffold protein for E3 ubiquitin ligase complexes. Ectopic expression of CUL3 increases the ubiquitination of RhoGDI1. Furthermore, potassium channel tetramerization domain containing 5 (KCTD5) also binds to RhoGDI1 and increases its interaction with CUL3. Ectopic expression of KCTD5 increases the ubiquitination of RhoGDI1, whereas its knockdown by RNA interference has the opposite effect. Depletion of KCTD5 or expression of dominant-negative CUL3 (DN-CUL3) enhances the stability of RhoGDI1. Our findings reveal a previously unknown mechanism for controlling RhoGDI1 degradation that involves a CUL3/KCTD5 ubiquitin ligase complex.