• 호남수학학술지
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• 제38권4호
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• pp.675-683
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• 2016

We give the representation of Fibonacci quaternions for convenient calculus. We research the corresponding properties of Fibonacci quaternions and some examples of a function with values in modified Fibonacci quaternions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권2호
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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 $C^2{\times}C^2$.

• East Asian mathematical journal
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• 제31권1호
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• pp.119-126
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• 2015

The aim of this paper is to research certain properties of conic regular functions of conic quaternion variables in $\mathbb{C}^2$. We generalize the properties of conic regular functions and the Cauchy theorem of conic regular functions in conic quaternion analysis.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권1호
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• pp.97-104
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• 2016

We give representations of differential operators and rules for addition and multiplication of dual quaternions. Also, we research the notions and properties of a regular function and a corresponding harmonic function with values in dual quaternions of Clifford analysis.

• 대한수학회보
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• 제54권2호
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• pp.583-592
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• 2017

The paper gives the regularity of dual quaternionic functions and the dual Cauchy-Riemann system in dual quaternions. Also, the paper researches the polar representation and properties of a dual quaternionic function and their regular quaternionic functions.

• 호남수학학술지
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• 제35권4호
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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.

• 호남수학학술지
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• 제39권2호
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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.

• East Asian mathematical journal
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• 제33권3호
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• pp.309-315
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• 2017

In this paper, we investigate the regularities of the hyper-complex valued functions of the split quaternion variables. We define several differential operators for the split qunaternionic function. We research several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the corresponding Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion field.

• 호남수학학술지
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• 제36권4호
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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.