On the regions containing all the zeros of polynomials and related analytic functions

Authors

  • Nisar Ahmad Rather University of Kashmir, Srinagar, 190006, India
  • Ishfaq Dar University of Kashmir, Srinagar, 190006, India
  • Aaqib Iqbal University of Kashmir, Srinagar, 190006, India

DOI:

https://doi.org/10.21638/spbu01.2021.212

Abstract

In this paper, by using standard techniques we shall obtain results with relaxed hypothesis which give zero bounds for the larger class of polynomials. Our results not only generalizes several well-known results but also provide better information about the location of zeros. We also obtain a similar result for analytic functions. In addition to this, we show by examples that our result gives better information on the zero bounds of polynomials than some known results.

Keywords:

polynomials, zeros, complex domain

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References

Литература

1. Cauchy A.L. Exercises de math´ematique. Oeuvres 9, 122 (1829).

2. Marden M. Geometry of Polynomials. In: Math. Surveys, no. 3. Amer. Math. Soc. Providence, RI (1966).

3. Milovanovi´c G.V., Mitrinovi´c D.S., Rassias Th.M. Topics in Polynomials: Extremal Problems, Inequalities, Zeros. World Scientific Publications (1994).

4. Joyal A., Labelle G., Rahman Q.I. On the Location of Zeros of Polynomials. Canadian Math. Bull. 10, 53–63 (1967). https://doi.org/10.4153/CMB-1967-006-3

5. Aziz A., Zargar B.A. Some Extensions of Enestrom-Kakeya Theorem. Glasnick Matematicki 31, 239–244 (1996).

6. Rahman Q. I., Schmeisser G. Analytic theory of Polynomials. Clarendon Press Oxford, 243–270 (2002).

7. Aziz A., Shah W.M. On the location of zeros of polynomials and related analytic functions. Nonlinear Studies 6, 91–101 (1999).

References

1. Cauchy A.L. Exercises de math´ematique. Oeuvres 9, 122 (1829).

2. Marden M. Geometry of Polynomials. In: Math. Surveys, no. 3. Amer. Math. Soc. Providence, RI (1966).

3. Milovanovi´c G.V., Mitrinovi´c D.S., Rassias Th.M. Topics in Polynomials: Extremal Problems, Inequalities, Zeros. World Scientific Publications (1994).

4. Joyal A., Labelle G., Rahman Q.I. On the Location of Zeros of Polynomials. Canadian Math. Bull. 10, 53–63 (1967). https://doi.org/10.4153/CMB-1967-006-3

5. Aziz A., Zargar B.A. Some Extensions of Enestrom-Kakeya Theorem. Glasnick Matematicki 31, 239–244 (1996).

6. Rahman Q. I., Schmeisser G. Analytic theory of Polynomials. Clarendon Press Oxford, 243–270 (2002).

7. Aziz A., Shah W.M. On the location of zeros of polynomials and related analytic functions. Nonlinear Studies 6, 91–101 (1999).

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Published

2021-07-21

How to Cite

Rather, N. A., Dar, I., & Iqbal, A. (2021). On the regions containing all the zeros of polynomials and related analytic functions. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8(2), 331–337. https://doi.org/10.21638/spbu01.2021.212

Issue

Vol. 8 No. 2 (2021)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.