• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.57-63
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• 2015

We define a hyperholomorphic function with values in split quaternions, provide split hyperholomorphic mappings on ${\Omega}{\subset}\mathbb{C}^2$ and research the properties of split hyperholomorphic functions.

• 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.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.921-932
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• 2014

The aim of this paper is to define hyperholomorphic functions with dual sedenion variables on $\mathcal{S}{\times}\mathcal{S}$, where $$\mathcal{S}{\sim_=}\mathbb{C}^8$$. By the condition of harmonicity, we research properties of hyperholomorphic functions of dual sedenion variables in Clifford analysis.

• East Asian mathematical journal
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• v.30 no.3
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• pp.361-369
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• 2014

The aim of this paper is to de ne hyperholomorphic function with dual octonion variables in $\mathbb{C}^4{\times}\mathbb{C}^4$. We characterize properties of dual octonion variables in Clifford analysis.

• East Asian mathematical journal
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• v.28 no.5
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• pp.553-559
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• 2012

The noncommutative extension of the complex numbers for the four dimensional real space is a quaternion. R. Fueter, C. A. Deavours and A. Subdery have developed a theory of quaternion analysis. M. Naser and K. N$\hat{o}$no have given several results for integral formulas of hyperholomorphic functions in Clifford analysis. We research the properties of hyperholomorphic functions on $\mathbb{C}^2{\times}\mathbb{C}^2$.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.809-817
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• 2013

We research properties of a corresponding Cauchy theorem of hyperholomorphic functions in an open set of product complex spaces, in the sense of complex Clifford analysis.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.91-98
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• 2007

We give definitions of hyperholomorphic functions of quaternionic functions of two quaternionic variables. We investigate properties of hyperholomorphic functions on quaternion analysis, and obtain equivalence relations for domains of hyperholomorphy and hyper Stein domains in a domain of $C^2{\times}C^2$.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.543-553
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• 2014

The aim of this paper is to define hyperholomorphic functions with dual octonion variables on $\mathbb{C}^4{\times}\mathbb{C}^4$ in another way. Using condition of harmonicity, we research properties of functions of dual octonion variables in Clifford analysis.

• East Asian mathematical journal
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• v.29 no.3
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• pp.293-302
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• 2013

We research properties of ternary numbers and hyperholomorphic functions with values in $\mathbb{C}$(2). We represent reduced quaternion numbers and obtain some propertries in dual reduced quaternion systems in view of Clifford analysis. Moreover, we obtain Cauchy theorems with respect to dual reduced quaternions.

• The Pure and Applied Mathematics
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• v.20 no.2
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• pp.129-136
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• 2013

We research properties of ternary numbers with values in ${\Lambda}(2)$. Also, we represent dual ternary numbers in the sense of Clifford algebras of real six dimensional spaces. We give generation theorems in dual ternary number systems in view of Clifford analysis, and obtain Cauchy theorems with respect to dual ternary numbers.