• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.691-700
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• 2009

We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.217-225
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• 2012

A generalized quadratic fuzzy set is a generalization of a quadratic fuzzy number. Zadeh defines the probability of the fuzzy event using the probability. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized quadratic fuzzy sets.

• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.99-108
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• 2017

In this paper we construct quadratic ${\beta}-algebras$ on a field, and we discuss both linear-quadratic ${\beta}-algebras$ and quadratic-linear ${\beta}-algebras$ in a field. Moreover, we discuss some relations of binary operations in ${\beta}-algebras$.

• Journal of the Korean Mathematical Society
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• v.58 no.4
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• pp.849-871
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• 2021

A (positive definite integral) quadratic form is called even 2-universal if it represents all even quadratic forms of rank 2. In this article, we prove that there are at most 55 even 2-universal even quadratic forms of rank 5. The proofs of even 2-universalities of some candidates will be given so that exactly 20 candidates remain unproven.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.261-272
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• 2001

In this paper we prove the stability of the generalized quadratic equation f(x+y)+g(x-y)-2f(x)-2g(y)=0 in the spirit of Hyers, Ulam and Rassias.

• Korean Journal of Mathematics
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• v.11 no.1
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• pp.57-64
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• 2003

We define $Z_16$ quadratic residue codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over a field.

• Honam Mathematical Journal
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• v.29 no.2
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• pp.205-212
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• 2007

In this paper, we give some properties of the dynamics of quadratic rational maps. Using the properties we present the algorithm for drawing the Julia sets of the quadratic rational maps. We illustrate that they are fractals by computer graphics.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.263-274
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• 2006

In this paper, we prove the Hyers-Ulam-Rassias stability of the quadratic mapping in generalized quasi-Banach spaces, and of the quadratic mapping in generalized p-Banach spaces.

• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.237-247
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• 2006

In this paper we solve the Hyers-Ulam stability problem for quadratic functional equations on restricted domains, and then obtain an asymptotic behavior of quadratic mappings on restricted domains.

• International Journal of CAD/CAM
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• v.9 no.1
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• pp.55-60
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• 2010

Quadratic B$\acute{e}$zier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic B$\acute{e}$zier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing $G^1$ quadratic B$\acute{e}$zier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the $G^1$ quadratic B$\acute{e}$zier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.