scholarly journals The Regularity of Functions on Dual Split Quaternions in Clifford Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ji Eun Kim ◽  
Kwang Ho Shon
Keyword(s):  
Power Series ◽  
Clifford Analysis ◽  
Differential Operators ◽  
Regular Function ◽  
Split Quaternion ◽  
Split Quaternions ◽  
Cauchy Riemann ◽  
Dual Split Quaternion

This paper shows some properties of dual split quaternion numbers and expressions of power series in dual split quaternions and provides differential operators in dual split quaternions and a dual split regular function onΩ⊂ℂ2×ℂ2that has a dual split Cauchy-Riemann system in dual split quaternions.

Regular functions on dual split quaternions in Clifford analysis

Filomat ◽  
2017 ◽  
Vol 31 (1) ◽  
pp. 17-27
Author(s):  
Ji Kim ◽  
Kwang Shon
Keyword(s):  
Power Series ◽  
Clifford Analysis ◽  
Differential Operators ◽  
Split Quaternions ◽  
Regular Functions ◽  
Cauchy Riemann

This paper shows expressions of a power series for the form of dual split quaternions and provides differential operators in dual split quaternions. The paper also represents a power series of dual split regular functions by using a dual split Cauchy-Riemann system in dual split quaternions.

scholarly journals Inverse mapping theory on split quaternions in Clifford analysis

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1883-1890 ◽  
Author(s):  
Ji Kim ◽  
Kwang Shon
Keyword(s):  
Clifford Analysis ◽  
Regular Function ◽  
Inverse Mapping ◽  
Split Quaternions ◽  
Cauchy Riemann ◽  
Mapping Theory

We give a split regular function that has a split Cauchy-Riemann system in split quaternions and research properties of split regular mappings with values in S. Also, we investigate properties of an inverse mapping theory with values in split quaternions.

scholarly journals Regularity of Functions on the Reduced Quaternion Field in Clifford Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ji Eun Kim ◽  
Su Jin Lim ◽  
Kwang Ho Shon
Keyword(s):  
Exponential Function ◽  
Clifford Analysis ◽  
Regular Function ◽  
Regular Functions ◽  
Quaternion Field ◽  
Hypercomplex Structure ◽  
Cauchy Riemann

We define a new hypercomplex structure ofℝ3and a regular function with values in that structure. From the properties of regular functions, we research the exponential function on the reduced quaternion field and represent the corresponding Cauchy-Riemann equations in hypercomplex structures ofℝ3.

A family of hyper-Bessel functions and convergent series in them

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Jordanka Paneva-Konovska
Keyword(s):  
Power Series ◽  
Bessel Function ◽  
Classical Theory ◽  
Bessel Functions ◽  
Differential Operators ◽  
Arbitrary Order ◽  
Convergent Series ◽  
Multi Index ◽  
Fatou Theorem ◽  
Convergence Of Series

AbstractThe Delerue hyper-Bessel functions that appeared as a multi-index generalizations of the Bessel function of the first type, are closely related to the hyper-Bessel differential operators of arbitrary order, introduced by Dimovski. In this work we consider an enumerable family of hyper-Bessel functions and study the convergence of series in such a kind of functions. The obtained results are analogues to the ones in the classical theory of the widely used power series, like Cauchy-Hadamard, Abel and Fatou theorem.

scholarly journals Some Fixed Points Results of Quadratic Functions in Split Quaternions

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Young Chel Kwun ◽  
Mobeen Munir ◽  
Waqas Nazeer ◽  
Shin Min Kang
Keyword(s):  
Fixed Points ◽  
Quadratic Polynomial ◽  
Quadratic Functions ◽  
Split Quaternion ◽  
Quadratic Polynomials ◽  
Split Quaternions

We attempt to find fixed points of a general quadratic polynomial in the algebra of split quaternion. In some cases, we characterize fixed points in terms of the coefficients of these polynomials and also give the cardinality of these points. As a consequence, we give some simple examples to strengthen the infinitude of these points in these cases. We also find the roots of quadratic polynomials as simple consequences.

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