Number of zeros of a polynomial (Lacunary-type) in a disk

• Autorzy: Qasim I. , Rasool T. , Liman A.

Identyfikatory

DOI

10.7862/rf.2018.13

• Języki publikacji: EN

Abstrakty

EN

The problem of finding out the region which contains all or a prescribed number of zeros of a polynomial [wzór] has a long history and dates back to the earliest days when the geometrical representation of complex numbers was introduced. In this paper, we present certain results concerning the location of the zeros of Lacunary-type polynomials [wzór] in a disc centered at the origin.

Słowa kluczowe

EN

zeros; Lacunary polynomial; prescribed region

PL

zera; wielomian

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2018
• Tom: Vol. 41
• Strony: 181--194
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Qasim I.

• Department of Mathematics, National Institute of Technology, Srinagar - 190006, India

autor

Rasool T.

• Department of Mathematics, National Institute of Technology, Srinagar - 190006, India

autor

Liman A.

• Department of Mathematics, National Institute of Technology, Srinagar - 190006, India

Bibliografia

• [1] I. Ahmad, T. Rasool, A. Liman, Zeros of certain polynomials and analytic functions with restricted coefficients, Journal of Classical Analysis 2 (2014) 149-157.
• [2] T. Chan, M. Malik, On the Erdös-Lax Theorem, Proceeding of Indian Academy of Sciences 92 (1983) 191-193.
• [3] K.K. Dewan, Extremal properties and coefficient estimates for polynomials with restricted zeros and on location of zeros of polynomials, Ph.D Thesis, IIT Delhi, 1980.
• [4] N.K. Govil, Q.I. Rahman, On the Eneström Kakeya theorem, Tohoku Math. J. 20 (1968) 126-136.
• [5] E. Landau, Über den Picardschen Satz, Vierteljahrsschrift Naturforsch. Gesellschaft Zürcher & Furrer 51 (1906) 252-318.
• [6] E. Landau, Sur quelques generalisations du theoreme de M. Picard, Ann. Ecole Norm. 24 (3) (1907) 179-201.
• [7] A. Liman, W.M. Shah, T. Rasool, Some new generalizations of Eneström Kakeya theorem, Nonlinear Functional Analysis and Applications 17 (2) (2012) 235-248.
• [8] A. Liman, I.A. Faiq, Bounds for the zeros of polynomial, International Journal of Modern Mathematical Sciences 13 (1) (2015) 12-16.
• [9] M. Marden, Geometry of Polynomials, Math. Surveys No. 3, Amer. Math. Soc. Providence R. I., 1949.
• [10] G.V. Milovanovic, D.S. Mitrinovic, Th. M. Rassias, Topics in Polynomials, Extermal Problems, Inequalities, Zeros, World Scientific, Singapore, 1994.
• [11] Q.G. Mohammad, On the zeros of the polynomials, Amer. Math. Monthly 72 (6) (1965) 631-633.
• [12] Q.I. Rahman, S. Schmeisser, Analytic Theory of Polynomials, Oxford University press, New York, 2002.
• [13] W.M. Shah, A. Liman, On Eneström Kakeya theorem and related analytic functions, Proc. Indian Acad. Sci.( Math Sci.) 117 (3) (2007) 359-370.
• [14] E.C. Titchmarsh, The Theory of Functions, 2nd ed. Oxford Univ. Press, London, 1939.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).