• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.197-206
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• 2006

In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated. We introduce quasi-2-normed spaces and quasi-(2; p)-normed spaces, and investigate the properties of quasi-2-normed spaces and quasi-(2; p)-normed spaces.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.287-328
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• 2016

In the current work, we define and find the general solution of the decic functional equation g(x + 5y) - 10g(x + 4y) + 45g(x + 3y) - 120g(x + 2y) + 210g(x + y) - 252g(x) + 210g(x - y) - 120g(x - 2y) + 45g(x - 3y) - 10g(x - 4y) + g(x - 5y) = 10!g(y) where 10! = 3628800. We also investigate and establish the generalized Ulam-Hyers stability of this functional equation in Banach spaces, generalized 2-normed spaces and random normed spaces by using direct and fixed point methods.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.2
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• pp.215-222
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• 2005

In this paper, the notion of a generalized quasi-normed space is introduced and its completion is investigated.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2061-2070
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• 2013

In this paper, we investigate the generalized HyersUlam-Rassias stability of the following additive functional equation $$2\sum_{j=1}^{n}f(\frac{x_j}{2}+\sum_{i=1,i{\neq}j}^{n}\;x_i)+\sum_{j=1}^{n}f(x_j)=2nf(\sum_{j=1}^{n}x_j)$$, in quasi-${\beta}$-normed spaces.

• The Pure and Applied Mathematics
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• v.26 no.2
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• pp.85-97
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• 2019

In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a $quasi-{\beta}-normed$ space with both the direct estimation method and the fixed point approach.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.291-308
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• 2007

The motivation of this paper is to present a new and interesting notion of intuitionistic fuzzy n-normed linear space. Cauchy sequence and convergent sequence in intuitionistic fuzzy n-normed linear space are introduced and we provide some results onit. Furthermore we introduce generalized cartesian product of the intuitionistic fuzzy n-normed linear space and establish some of its properties.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.437-451
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• 2011

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

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.339-348
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• 2014

In this paper, we investigate the solution of the following functional inequality $${\parallel}f(x)+f(y)+f(az),\;w{\parallel}{\leq}{\parallel}f(x+y)-f(-az),\;w{\parallel}$$ for some xed non-zero integer a, and prove the generalized Hyers-Ulam stability of it in non-Archimedean 2-normed spaces.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.887-900
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• 2013

In this paper, we investigate the stability for the functional equation f(3x+y)-3f(2x+y)+3f(x+y)-f(y)=0 in the sense of M. S. Moslehian and Th. M. Rassias.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.353-363
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• 2015

In this paper, we investigate the functional equation f(3x+y)+f(3x-y) = f(x+2y)+2f(x-y)+6f(2x)+3f(x)-6f(y) and prove the generalized Hyers-Ulam stability for it in non-Archimedean normed spaces.