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On the zeros of polynomials and their generalized derivative | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 04 شهریور 1404 اصل مقاله (349.16 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.35648.5300 | ||
| نویسندگان | ||
| Mohammad Ibrahim Mir؛ Shahadat Ali* ؛ Jamina Banoo | ||
| Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India | ||
| تاریخ دریافت: 26 مهر 1403، تاریخ پذیرش: 07 آذر 1403 | ||
| چکیده | ||
| In this paper, we present findings on the placement of zeros of generalized derivative of polynomials, drawing parallels to those observed in the ordinary derivative of polynomials. Mathematicians have broadened the scope of the Gauss-Lucas Theorem, a classic principle that deals with zero location in polynomials and their derivatives. The new work expands it to cover convex linear combinations of incomplete polynomials. | ||
| کلیدواژهها | ||
| Polynomials؛ Half-plane؛ Specht Theorem؛ Gauss-Lucas Theorem؛ Generalized Derivative؛ Grace Heawood Theorem | ||
| مراجع | ||
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[1] A. Aziz, On the zeros of a polynomials and its derivative, Bull. Aust. Math. Soc. 31 (1985), no. 4, 245–255. [2] A.L. Cauchy, Exercises de mathematique, Oeuvres 9 (1829), 122. 2000. [3] J.L. Dıaz-Barrero and J.J. Egozcue, A generalization of the Gauss-Lucas theorem, Czech. Math. J. 58 (2008), no. 2, 481–486. [4] M. Marden, The Geometry of the Zeros of a Polynomial in a Complex Variable, American Mathematical Society, Rhode Island, 1966. [5] M.I. Mir, I.A. Wani, and I. Nazir, On the zeros and critical points of a polynomial, Math. Anal. Contemp. Appl. 4 (2022), no. 1, 25–28. [6] J. Sz-Nagy, Verallgemeinerung der derivierten in der geometric der polynome, Acta Univ. Szeged. Sect. Sci. Math. 13 (1950), 169–178. [7] Q.I. Rahman and G. Schmeisser, Analytic Theory of Polynomials, Oxford University Press Inc., New York, 2002. | ||
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