Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE NUMBER OF ZEROS OF BICOMPLEX ENTIRE FUNCTIONS

  • Shahbaz Mir (Department of Mathematics, National Institute of Technology) ;
  • Abdul Liman (Department of Mathematics, National Institute of Technology)
  • Received : 2023.01.29
  • Accepted : 2023.06.21
  • Published : 2023.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper portrays the results on bicomplex entire functions that are concerned with the positioning of zeros of Eneström-Kakeya type. Moreover, some examples are provided to validate our results.

Keywords

References

  1. M. Bidkham and S. Ahmadi, Generalization of the Gauss-Lucas theorem for bicomplex polynomials, Turk. J. Math. 41 (2017), 1618-1627.  https://doi.org/10.3906/mat-1512-19
  2. N. Carney, R. Gardner, R. Keaton, and A. Powers, The Enestrom-Kakeya theorem of a quaternionic variable, J. Appl. Theory 250 (2020), 105-325. 
  3. J. B. Conway, Function of one complex variable, 2nd edition Springer-Verlag, 1978. 
  4. N. K. Govil and Q. I. Rahman, On the Enestrom-Kakeya theorem II, Tohoku Math. J. 20 (1968), 126-136.  https://doi.org/10.2748/tmj/1178243172
  5. A. Joyal, G. Labelle, and Q. I. Rahman, On the location of zeros of polynomials, Can. Math. Bull. 10 (1967), 53-63.  https://doi.org/10.4153/CMB-1967-006-3
  6. J. Kumar and R. K. Srivastava, On a class of entire bicomplex sequences, South East Asian J. Math. Sci. 5 (3) (2007), 47-67. 
  7. M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa, and A. Vajiac, Bi-complex Holomorphic Functions, The Algebra, Geometry and Analysis of Bi-complex Numbers. Birkhauser (2015). 
  8. M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa, and A. Vajiac, Bi-complex numbers and their elementary functions, Cubo 14 (2) (2012), 61-80.  https://doi.org/10.4067/S0719-06462012000200004
  9. M. Marden, Geometry of Polynomials, Math. Surveys, No. 3, Amer. Math. Soc. (1966). 
  10. A. A Pogorui and R. M. Rodriguez-dagnino, On the set of zeros of bi-complex polynomials, Complex Variables and Elliptic Equations 51:7 (2006), 725-730.  https://doi.org/10.1080/17476930600757139
  11. G. B. Price, An Introduction to Multicomplex Spaces and Functions, Monographs and Textbooks in Pure and Applied Mathematics, 140, Marcel Dekker, Inc., New York, 1991. 
  12. C. Segre, Le rappresentation reali delle forme complesse e gli enti iperalgebrici, Math. Ann. 40 (1892), 413-467.  https://doi.org/10.1007/BF01443559
  13. W. M. Shah and A. Liman, On Enestrom-Kakeya theorem and related analytic functions, Proc. Indian Acad. Sci. 3 (2007), 359-370.