• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1721-1728
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• 2015

We give certain properties of elements in a coset group with hypercomplex numbers and research a monogenic function and a Clifford regular function with values in a coset group by defining differential operators. We give properties of those functions and a power of elements in a coset group with hypercomplex numbers.

• East Asian mathematical journal
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• v.29 no.5
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• pp.521-527
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• 2013

The aim of this paper is to define hyperholomorphic function with sedenion variables in $\mathbb{C}^8$ and research the properties of hyperholomorphic functions of sedenion variables. We generalize the properties of hyperholomorphic functions in sedenionic analysis.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.825-841
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• 2020

We characterize bicomplex holomorphic functions from several estimates. Originally, Riley [5] studied such problems in local case. In our study, we treat global estimates on various unbounded domains. In many cases, we can determine the explicit form of a function.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.569-575
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• 2015

In this paper, we research some properties of quaternionic regular functions in Clifford analysis. We investigate the corresponding Cauchy-Riemann system and find regularities of some hypercomplex valued functions.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.307-315
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• 2017

In this paper, we aim to compare the differentials with the regularity of the hypercomplex valued functions in Clifford analysis. For three kinds of conjugation of the bicomplex numbers, we define the differentials of the bicomplex number functions by the naive approach. And we investigate some relations of the corresponding Cauchy-Riemann system and the conditions of the differentiable functions in the bicomplex number system.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.685-692
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• 2016

The aim of this paper is to investigate the differentials of the hypercomplex valued functions in Clifford analysis. Like as the differentials defined by the naïve approach in one complex variable analysis, we define the differentials of functions with values in ternary number functions by same ways. And we survey the properties of each differential with respect to a non-commutativity of the skew field.