• 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.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.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.81-92
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• 2019

We introduce a reciprocal-negative Fermat's equation generalized with constants coefficients and investigate its stability in a quasi-${\beta}$-normed space.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.29-46
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• 2019

We introduce a generalized cubic functional equation and investigate the Hyers-Ulam stability of the cubic functions as solutions to the generalized cubic functional equation on a quasi-fuzzy anti-${\beta}$-Banach space by both the direct method and the fixed point method.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.1-14
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• 2019

We prove the generalized Hyers-Ulam-Rassias stability problem of the quadratic functional equation with involution in the fuzzy quasi ${\beta}$-normed space by using the fixed point method.

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.93-104
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• 2024

In this paper, we will prove a fixed point theorem for self-mappings on a generalized quasi-ordered metric space which is a generalization of the concept of a generalized metric space with a partial order and we investigate a genralized quasi-ordered metric space related with fuzzy normed spaces. Further, we prove the stability of some functional equations in fuzzy normed spaces as an application of our fixed point theorem.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1421-1433
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• 2011

In this paper, using a fixed point approach, the generalized Hyeres-Ulam stability of the following quadratic functional equation $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=3(f(x)+f(y)+f(z))$ will be studied, where f is a function from abelian group G into a quasi-${\beta}$-normed space and ${\sigma}$ is an involution on the group G. Next, we consider its pexiderized equation of the form $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=g(x)+g(y)+g(z)$ and its generalized Hyeres-Ulam stability.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.319-326
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• 2020

In this paper, we establish a general solution of the following functional equation $$mf\({\sum\limits_{k=1}^{n}}x_k\)+{\sum\limits_{t=1}^{m}}f\({\sum\limits_{k=1}^{n-i_t}}x_k-{\sum\limits_{k=n-i_t+1}^{n}}x_k\)=2{\sum\limits_{t=1}^{m}}\(f\({\sum\limits_{k=1}^{n-i_t}}x_k\)+f\({\sum\limits_{k=n-i_t+1}^{n}}x_k\)\)$$ where m, n, t, i_t ∈ ℕ such that 1 ≤ t ≤ m < n. Also, we study Hyers-Ulam-Rassias stability for the generalized quadratic functional equation with n-variables and m-combinations form in quasi-𝛽-normed spaces and then we investigate its application.