• 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.26 no.4
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• pp.915-922
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• 2013

In this paper, we investigate some properties of 2-norm midpoints and 2-normed equalities in 2-normed spaces.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.387-400
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• 2009

We establish a new strategy to study the Hyers-Ulam-Rassias stability of the Cauchy and Jensen equations in non-Archimedean normed spaces. We will also show that under some restrictions, every function which satisfies certain inequalities can be approximated by an additive mapping in non-Archimedean normed spaces. Some applications of our results will be exhibited. In particular, we will see that some results about stability and additive mappings in real normed spaces are not valid in non-Archimedean normed spaces.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.137-147
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• 2012

In this paper we introduce some new double sequence spaces via ideal convergence and an Orlicz function in $n$-normed spaces and examine some properties of the resulting spaces.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.315-327
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• 2010

We give a xed point approach to the generalized Hyers-Ulam stability of the cubic equation f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 12f(x) in non-Archimedean normed spaces. We will give an example to show that some known results in the stability of cubic functional equations in real normed spaces fail in non-Archimedean normed spaces. Finally, some applications of our results in non-Archimedean normed spaces over p-adic numbers will be exhibited.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.623-633
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• 2009

The classical Mazur-Ulam theorem states that every surjective isometry between real normed spaces is affine. In this paper, we study 2-isometries in probabilistic 2-normed spaces.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.161-173
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• 2020

We introduce statistically localized sequences in 2-normed spaces and give some main properties of statistically localized sequences. Also, we prove that a sequence is statistically Cauchy sequence if and only if its statistical barrier is equal to zero. Moreover, we define the uniformly statistically localized sequences on 2-normed spaces and investigate its relationship with statistically Cauchy sequences.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.311-319
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• 2015

In this article, we consider a modified quadratic functional equation and then investigate its generalized Hyers-Ulam stability theorem in quasi-${\beta}$-normed spaces.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.211-225
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• 2021

In the present paper we introduce some sequence spaces over n-normed spaces defined by fractional difference operator and Musielak-Orlicz function 𝓜 = (𝕱_i). We also study some topological properties and prove some inclusion relations between these spaces.

• 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.