On the number of zeros of a polynomial in a region

• Autorzy: Kareem K. A. , Mogbademu A. A.

Identyfikatory

DOI

10.1515/fascmath-2016-0016

• Języki publikacji: EN

Abstrakty

EN

In this paper, we impose restrictions on the complex coefficients of a polynomial in order to give bounds concerning the number of zeros in a specific region of the complex plane. Our results generalize and refine a good number of results in this area of research.

Słowa kluczowe

EN

polynomial; zeros of polynomials; monotonicity; disk

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2016
• Tom: Nr 57
• Strony: 53--65
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Kareem K. A.

• Department of Mathematics, University of Lagos, Nigeria

autor

Mogbademu A. A.

• Department of Mathematics, University of Lagos, Nigeria

Bibliografia

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• [2] Dewan K.K., Extremal Properties and Coefficient Estimates for Polynomials with Restricted Zeros and on Location of Zeros of Polynomials, Ph.D. Thesis, Indian Institutes of Technology, Delhi, 1980.
• [3] Dewan K.K., Bidkham M., On the Eneström-Kakeya theorem, Journal of Mathematical Analysis and Applications, 180(1993), 29-36.
• [4] Gardner R.B., Govil N.K., On the Location of the Zeros of a Polynomial, Journal of Approximation Theory, 78(2), (1994), 286-292.
• [5] Gardner R.B., Shields B., The Number of Zeros of A Polynomials in A Disk, Journal of Classical Analysis, 3(2), (2013), 167-176.
• [6] Govil N.K., Rahman Q.I., On the Eneström-Kakeya theorem, Tohoku Mathematics Journal, 20(1968), 126-136.
• [7] Gulzar M.H., Bounds For the zeros and Extremal Properties of Polynomials, Ph.D. Thesis, University of Kashmir, Srinagar, 2012.
• [8] Kareem K.A., Mogbademu A.A., On the number of zeros of certain polynomials, Mathematica Moravica, (in press).
• [9] Milovanovic G.V., Mitrinovic D.S., Rassias TH.M., Topics in Polynomials: Extremal Problems, Inequalities, Zeros, Singapore: World Scientific Publishing, 1994.
• [10] Mogbademu A.A., Hans S., Adepoju J.A., A note on Eneström-Kakeya Theorem, Nonlinear Functional Analysis and Applications, 20(1)(2015), 139-145.
• [11] Mogbademu A.A., Hans S., Adepoju J.A., Some extensions and generalizations of Eneström-Kakeya theorem, Journal of The Nigerian Mathematical Society, 34(2), (2015), 243-248.
• [12] Mohammad Q.G., On the zeros of the polynomials, American Mathematical Monthly, 72(6), (1965), 631-633.
• [13] Pukhta M.S., On the zeros of a polynomial, Applied Mathematics, 2(2011), 1356-1358.
• [14] Rahman Q.I., Schmeisser G., Analytic Theory of Polynomials, Oxford: Clarendon Press, 2002.
• [15] Titchmarsh E.C., The Theory of Functions, 2nd Edition, Oxford University Press, London, 1939.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.