• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.397-403
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• 2008

In this paper, we modify L. $C\breve{a}dariu$ and V. Radu's result for the stability of the monomial functional equation $\sum\limits_{n=0}^{n}n\;C_i(-1)^{n-i}f(ix+y)-n!f(x)=0$ in the sense of Th. M. Rassias. Also, we investigate the superstability of the monomial functional equation.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.269-275
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• 2021

Let ℝ be the set of real numbers, f, g : ℝ → ℝ and �� ≥ 0. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation $$f({\sqrt[n]{x^N+y^N}})=f(x)g(y)$$ for all x, y ∈ ℝ, i.e., we investigate the functional inequality $$\|f({\sqrt[n]{x^N+y^N}})-f(x)g(y)\|{\leq}{\epsilon}$$ for all x, y ∈ ℝ.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.777-785
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• 2010

Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X $\rightarrow$ Y, which satisfies the inequality ${\parallel}{\Delta}_x^nf(y)\;-\;n!f(x){\parallel}\;{\leq}\;\varphi(x,y)$ for suitable control function $\varphi$, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of $t\;{\mapsto}\;f(tx)$ and $t\;{\mapsto}\;\varphi(tx,\;ty)$ imply the continuity of $t\;{\mapsto}\;M(tx)$.