• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.201-215
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $f(x+y+z+w)\;+\;2f(x)\;+\;2f(y)\;+\;2f(z)\;+\;2f(w)\;-\;f(x+y)\;-\;f(x+z)\;-\;f(x+w)\;-\;f(y+z)\;-\;f(y+w)\;-\;f(z+w)=0$.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.453-464
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• 2016

In this paper, we investigate the solution of the following functional inequality $$N(f(x)+f(y)+f(z),t){\geq}N(f(x+y+z),mt)$$ for some fixed real number m with $\frac{1}{3}$ < m ${\leq}$ 1 and using the fixed point method, we prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.51-63
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(2x+y)+f(2x-y)+2f(x)-f(x+y)-f(x-y)-2f(2x)=0$$.

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.161-172
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• 2011

In this paper we investigate the Hyers-Ulam stability of a Jensen type functional equation in multi-normed spaces and then extend the result to multi-normed left modules over a normed algebra A.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.703-712
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• 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.

• The Pure and Applied Mathematics
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• v.26 no.1
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• pp.49-58
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• 2019

In this paper, I prove the stability problem for a quadratic-cubic functional equation $$f(x+ky)-k^2f(x+y)-k^2f(x-y)+f(x-ky)+f(kx)-{\frac{k^3-3k^2+4}{2}}f(x)+{\frac{k^3-k^2}{2}}f(-x)=0$$ in modular spaces by applying the direct method.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.401-411
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• 2008

In this paper, we characterize Sobolev spaces $H^s(\mathbb{R}^n),\;s{\in}\mathbb{R}$ by the initial value of solutions of heat equation with a growth condition. By using an idea in its proof, we also discuss a stability problem for Cauchy functional equation in the Sobolev spaces.

• Journal of Families and Better Life
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• v.22 no.4
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• pp.105-113
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• 2004

The purpose of this study is to grasp the application tendency of interior accessories in Korean residential spaces. The main resources were selected documents and articles with pictures published 27 years, from 1976 to 2002, in Modern House, which is the first magazine for the residential space in Korea. The major findings are summarized as follows: 1) Interior accessories were investigated more for functional reasons than decorative reasons. Despite the belief that interior accessories are Primarily for decoration purposes, this study proves that the functional elements are more important as part of the Korean interior. 2) The kind and the amount of interior accessories applied in residential space were decreasing in most accessories as well as in master bedroom, and living rooms from 1994 to 2002. 3) The number of application to Korean traditional accessories in residential space decreases as time goes by. Although they were used as functional accessories as the role of antiques in present.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1511-1525
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• 2014

In this paper, we prove the generalized Hyers-Ulam stability results controlled by considering approximately mappings satisfying conditions much weaker than Hyers and Rassias conditions for radical quadratic and radical quartic functional equations in quasi-${\beta}$-normed spaces.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.1-9
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• 2023

Our aim in this paper is to give some new proofs to fixed point theorems due to Abdou [1] for mappings satisfying Reich type contractions in modular metric spaces. We removed the restriction that ω satisfies the ∆₂-type condition imposed on the results of [1]. Furthermore, Lemma 2.6 of [1] which was crucial in the proofs of the results of [1] is not needed in the proofs of our results. Our method of proof is simpler and interesting.