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Some generalized results of zeros of polar derivative of a polynomial | ||
Journal of Hyperstructures | ||
دوره 10، شماره 2، اسفند 2021، صفحه 129-136 اصل مقاله (297.78 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22098/jhs.2021.2646 | ||
نویسنده | ||
Ram Milan Singh* | ||
Department of Mathematics, Govt. P. G. college, Tikamgarh , P.O.Box 472001,Tikamgarh, India | ||
چکیده | ||
In the present paper, we further generalize and extend various results on zeroes of polar derivatives of polynomials due to Gulzar, Zargar and Akhter (2019), who gave extension and generalization of various results on Enestrom-Kakeya theorem established by various researchers in the literature. | ||
کلیدواژهها | ||
Zeros؛ polynomial؛ Enestrom-Kakeya theorem؛ polar derivative | ||
مراجع | ||
[1] A bdul Aziz, and Q. G. Mahammad, On the zeros of certain class of polynomials and related analytic functions, J. Math. Anal. Appl., 75 (1980), 495-502. [2] A bdul Aziz, and Q. G. Mahammad, , Cana. Math. Bull., ,Zero free regions for polynomials and some generalizations of Enestrom Kakeya theorem, Journal of Pure and Applied Algebra, 27(3) (1984) 265-272 [3] Bairagi, V. K, Saha, and T. K. Mishra, On the location of zeros of certain polynomials,Publication De L 'institut Mathematics, Nuvelle Serie, 99 113 (2016), 287-294. [4] G.Enestrom Remarquee sur un th'eor'eme relatif aux racines de l'equation an + … + a0 = 0 o"u toules coefficient sont et positifs, Toohoku Math. J, 18, 34 -36(1920). [5] C. Gangadhar, P.Ramulu and G.L Reddy Zero free regions of polar derivatives of polynomial with restricted coecients, IJ PEM, 4(30)(2016); 67 - 74.,. [6] M.H.Gulzar, B.A.Zargar, and R.Akhter On the zeros of the polar derivative of polynomial, Communication Nonlinear Analysis, 6(1)(2019); 32 - 39:. [7] S.Kakeya On the limits of the roots of an alegebraic equation with positive coefcient, T^ohoku Math. J, 2(1912-1913), 140-142.. [8] K.Praveen, and B.Krishna Reddy, A note on the zeroes of polar derivative of a polynomial, Malaya J ournal of Mathematik, vol 8. No.2, , (2020) 405 - 413 [9] P. Ramulu and G.L Reddy, On the zeros of polar derivatives, International J ournal of Recent Research in Mathematics Computer Science and Information Technology, 2(1)(2015),143-145. [10] G.L. Reddy, P.Ramulu and C.Gangadhar, , On the zeros of polar derivatives of polynomial Journal of Research in Applied Mathematics, 2(4)(2015); 07-10 | ||
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