• Korean Journal of Mathematics
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• v.28 no.3
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• pp.421-438
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• 2020

In this paper we enumerate all commutative single power cyclic hypergroups of order 4 and period 2. Moreover, we prove some interesting properties regarding cyclic hypergroups.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.63-80
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• 2019

In this paper, we consider a special hypergroup defined by Corsini and we name it Corsini hypergroup. First, we investigate some of its properties and find a necessary and sufficient condition for the productional hypergroup of Corsini hypergroups to be a Corsini hypergroup. Next, we study its regular relations, fundamental group and complete parts. Finally, we characterize all Corsini hypergroups of orders two and three up to isomorphism.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.693-698
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• 2014

Although the category NFHG of normal fuzzy hypergroups is not a topos, it forms a pseudo topos. Also we show that there are pseudo power objects in NFHG.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.579-585
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• 2017

Based on injectivity, we introduce some definitions in the category NFHG of normal fuzzy hypergroups. And we show that a complete normal fuzzy hypergroup is a weakly injective object in NFHG. Also we investigate weak injectivity in the comma category NFHG/K.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.689-697
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• 2022

In this paper, we study dual integrable representations of locally compact commutative hypergroups and give a sufficient and necessary condition for a dual integrable representation to have an admissible vector.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.285-295
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• 2006

We present a concept of negative definite functions on a commutative normal hypercomplex system $L_1$(Q, $m$) with basis unity. Negative definite functions were studied in [5] and [4] for commutative groups and semigroups respectively. The definition of such functions on Q is a natural generalization of that defined on a commutative hypergroups.

• Kyungpook Mathematical Journal
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• v.35 no.1
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• pp.17-23
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• 1995

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.231-242
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• 1998

On the basis of Heyer and Zeuner's results we will treat the central limit theorem for probability measures on hypergroup.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.513-526
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• 2010

In this paper, the theory of n-ary hypergroups and some applications of hyperalgebras (Fredholm-Voltra integral, copula) are studied. We define some new concepts of topological hyperdynamical systems, universal hyperdynamical systems and immersed universal hyperalgebra. Also, we present some results in this respect.

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.121-130
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• 1997

Our first theorem is concerned with the convergence of nets of Poisson measures on a hypergroup. As a corollary we obtain a characterization of Poisson measures. The second theorem gives a characterization of elementary Poisson measures.