Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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DERIVATIVES FOR THE LINEARITY OF TERNARY NUMBER VALUED FUNCTIONS

  • Kang, Han Ul (Department of Mathematics, Pusan National University) ;
  • Lee, Kwangho (Department of Mathematics, Pusan National University) ;
  • Shon, Kwang Ho (Department of Mathematics, Pusan National University)
  • Received : 2016.05.03
  • Accepted : 2016.10.05
  • Published : 2016.12.25
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Abstract

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.

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References

  1. H. S. Jung and K. H. Shon, Properties of hyperholomorphic functions on dual ternary numbers, J. Korean Soc. Math. Educ. Ser. B, Pure Appl. Math., 20 (2013), 129-136.
  2. H. S. Jung, S. J. Ha, K. H. Lee, S. M. Lim and K. H. Shon, Structures of hyperholomorphic functions on dual quaternion numbers, Honam Math. J., 35 (2013), 809-817. https://doi.org/10.5831/HMJ.2013.35.4.809
  3. J. E. Kim and K. H. Shon, The regularity of functions on dual split quaternions in Clifford analysis, Abstr. Appl. Anal., Art. ID 369430 (2014), 8 pages.
  4. J. E. Kim, S. J. Lim and K. H. Shon, Regular functions with values in ternary number system on the complex Clifford analysis, Abstr. Appl. Anal., Art. ID 136120 (2013), 7 pages.
  5. J. E. Kim, S. J. Lim and K. H. Shon, Regularity of functions on the reduced quaternion field in Clifford analysis, Abstr. Appl. Anal., Art. ID 654798 (2014), 8 pages.
  6. S. J. Lim and K. H. Shon, Split hyperholomorphic function in Cliiford analysis, J. Korea Soc. Math. Ser. B, Pure Appl. Math., 22 (2015), 57-63.
  7. M. E. Luna-Elizarraras and M. Shapiro, A survey on the (hyper-) derivatives in complex, quaternionic and Clifford analysis, Milan J. of Math., 79 (2011), 521-542. https://doi.org/10.1007/s00032-011-0169-0
  8. M. Naser, Hyperholomorphic functions, Siberian Math., 12 (1971), 959-968.