ESTIMATE OF DISK NOT CONTAINING ROOTS OF POLYNOMIAL FUNCTIONS
DOI:
https://doi.org/10.29121/granthaalayah.v10.i4.2022.4541Keywords:
Polynomials, Bounds, Modulus, Disk, Region, Zeros, RootsAbstract [English]
Let is a polynomial of degree. Also let coefficients of polynomial follow a certain pattern of decreasing or increasing in magnitude. Then we have many results for providing the regions containing all the roots of polynomial functions. Here, in this paper we prove a result that gives a disk or circular region containing no roots of function, Thereby our result finally gives annular region containing all roots of polynomial function and hence thereby improves the earlier proved .results.
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Aziz, A. and Mohammad, G.Q. (1984). Zero free regions for polynomials and some generalizations of Enestrom-Kakeya Theorem, Canad. Math. Bull., 27, 265-272. https://doi.org/10.4153/CMB-1984-040-3
Aziz, A. and Zargar, A. B., (1966). Some extensions of -Kakeya Theorem, Glasnik Mate., 51, 239-244.
Cauchy, A.l. (1829). Exercises de mathematique in oeuvres, Hachette Livre - BNF, 9, 122.
Daras, N. J. and Rassias, Th. (2015). Computation, Cryptography, and Network Security, Springer. https://doi.org/10.1007/978-3-319-18275-9
Dichler, K. (1996). A generalization of the Enestrom-Kakeya Theorem, Journal of Mathematical Analysis and Applications, 116, 473-488. https://doi.org/10.1016/S0022-247X(86)80012-9
Enestrom, G. (1920). Remarquee sur un Theoreme relatif aux racines de I' equation ou tous les coefficients sont reels et possitifs, Tohoku Mathematical Journal, 18, 34-36.
Hurwitz, A. (1913). Uber einen Satz des Herrn Kakeya, Tohoku Mathematical Journal, First Series, 4, 29-93.
Jain, V. K. (2009). On the zeros of polynomials, Proceedings - Mathematical Sciences, 119(1), 37-43. https://doi.org/10.1007/s12044-009-0004-5
Joyal, A. Labelle, G. and Rahman, Q. I. (1967). On the location of zeros of polynomials, Canad. Math. Bull., 10, 53-63. https://doi.org/10.4153/CMB-1967-006-3
Kakeya, S. (1912). On the limits of the roots of an algebraic equation with positive coefficients, Tohoku Mathematical Journal, First Series, 2, 140-142.
Lal, R. Kumar, S. and Hans, S. (2011). On the zeros of polynomials and analytic functions, Annales Universitatis Mariae Curie- Skłodowska, 2011 https://doi.org/10.2478/v10062-011-0008-3
Lal, R. (2019). Results for zeros of polynomial and analytic function, Jnanabha, 49(2), 15-21.
Marden, M, (1949). Geometry of the zeros of the polynomials in a complex variable, American Mathematical Society.
Milovanovic, G. V. Mitrinovic, D. S. and Rassias, T. h. M. (1994). Topics in polynomials, Extremal properties, Inequalities, Zeros., World Scientific Publishing Co. Singapore https://doi.org/10.1142/1284
Rahman, Q. I. and Schmeisser, G. (2002). Analytic Theory of Polynomials, Clarendon Press. Oxford.
Rassias, Th. Gupta, V. (2016). Mathematical Analysis, Approximation Theory and Their Applications, Springer Nature. https://doi.org/10.1007/978-3-319-31281-1
Rather, N. A. (1998). Extremal properties and location of zeros of polynomials.
Shah, W. M. and Liman, A. (2007). On Enestrom-Kakeya Theorem and related analytic functions, Proc. Proceedings Mathematical Sciences, 117 (3), 359-370. https://doi.org/10.1007/s12044-007-0031-z
Sheil-Small, T. (2002). Complex polynomials, Cambridge Univ. Press.
Vieira, R. S. (2017). On the number of roots of self-inversive polynomials on the complex unit circle. The Ramanujan Journal. 42(2),363-369.
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