Generalisations of EnestrÖ M-Kakeya Theorem for Complex Polynomial

Roshan Lal

doi:https://doi.org/10.14445/22315373/IJMTT-V56P546

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 5 | Year 2018 | Article Id. IJMTT-V56P546 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P546

Generalisations of EnestrÖ M-Kakeya Theorem for Complex Polynomial

Roshan Lal

Abstract

In this paper we have obtained some generalizations of EnestrÖ m -Kakeya Theorem regarding the region for location of zeros of polynomial in terms of restricted coefficients. Our results give not only zero free regions for polynomials but also the number of zeros that can lie in a prescribed region. Our result sharpens as well as generalizes the earlier known results.

Keywords

Polynomials; Zeros; Inequalities; Complex domain.

References

1. A. Aziz, On the zeros of composite polynomials, Pacific J. Maths., 103(1982),1-7.
2. Aziz, Growth of polynomials whose zeros are within or outside a circle, Bull. Austral. Math. Soc. 35(1987), 247-250.
3. N.K.Govil and Q.I.Rahman, On the EnestrÖ m-Kakeya Theorem, Tohoku Math. J., 20(1968) 126-136.
4. A. Joyal, G.Labelle and Q.I.Rahman, On the location of zeros of polynomials, Canad. Math. Bull., 10(1967) 53-63. 5. W.M.Shah, and A. Liman, On EnestrÖ m-Kakeya Theorem and related analytic functions, Proc. Indian Acad. Sci. (Math. Sci.) Vol-117, no-3, August 2007, 359-370.
6. E.C.Titchmarsh, The theory of functions, 2nd ed. Oxford Univ. Press, London, 1939.

Citation :

Roshan Lal, "Generalisations of EnestrÖ M-Kakeya Theorem for Complex Polynomial," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 5, pp. 344-351, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P546