The Journal of the Indian Mathematical Society

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Generalization of the Grace Theorem


Affiliations
1 University of Kashmir, Hazratbal Srinagar, 190006, India
2 Department of Mathematics, University of Kashmir, Hazratbal Srinagar, 190006, India
     

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In this paper we extend the theorem of Walsh and some results proved by R. Bakic to a half plane and complement of an open disk.

Keywords

Polynomial, Zeros, Grace Theorem, Apolar Polynomials.
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  • R. Bakic; Generalization of the Grace-Heawood Theorem; Publications de l Institut Mathematique Nouvelle serie, tome 93 (107)(2013), 65-67.

  • J. H. Grace; The zeros of a Polynomial; Proceedings of the Cambridge Philosophical Society, (11), (1902), 352-7.

  • Q.I. Rahman and G. Schmeisser; Analytic Theory of Polynomials; Oxford University Press, (2002), pp 108.

  • J.L. Walsh; On the Location of the Roots of Certain Types of Polynomials; Trans. Amer. Math. Soc. 24 (1922), 163-180.


Abstract Views: 353

PDF Views: 2




  • Generalization of the Grace Theorem

Abstract Views: 353  |  PDF Views: 2

Authors

N. A. Rather
University of Kashmir, Hazratbal Srinagar, 190006, India
Mohammad Ibrahim
Department of Mathematics, University of Kashmir, Hazratbal Srinagar, 190006, India

Abstract


In this paper we extend the theorem of Walsh and some results proved by R. Bakic to a half plane and complement of an open disk.

Keywords


Polynomial, Zeros, Grace Theorem, Apolar Polynomials.

References