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Bernstein-type inequalities for a zero-preserving operator on the space of polynomials | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 210، دوره 13، شماره 2، مهر 2022، صفحه 2597-2602 اصل مقاله (359.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.24630.2784 | ||
| نویسندگان | ||
| Mudassir Ahmad Bhat1؛ Suhail Gulzar* 2؛ Ravinder Kumar2 | ||
| 1Department of Mathematics, Chandigarh University,Mohali, Punjab, India | ||
| 2Department of Mathematics, Government College for Engineering & Technology Ganderbal, J& K, India | ||
| تاریخ دریافت: 01 مهر 1400، تاریخ بازنگری: 10 مهر 1400، تاریخ پذیرش: 07 تیر 1401 | ||
| چکیده | ||
| In this paper, we study zero-preserving character of a linear operator on the space of complex-polynomials which also preserve Bernstein-type inequalities for polynomials. | ||
| کلیدواژهها | ||
| Gauss Lucas theorem؛ Inequalities in the Complex Domain؛ Polynomials | ||
| مراجع | ||
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[1] A. Aziz, On the location of the zeros of certain composite polynomials, Pacific J. Math. 118 (1985), 17–26. [2] S.N. Bernstein, Sur. ´lordre de la meilleure appromation des functions continues par des Polynomes de degr´e donn´e, [3] S. Bernstein, Sur la limitation des d´eriv´ees des polynomes, C. R. Math. Acad. Sci. Paris 190 (1930), 338–340. [4] P.L. Cheung, T.W. Ng, J. Tsai and S.C.P. Yam, Higher-order, polar and Sz.-Nagy’s generalized derivatives of random polynomials with independent and identically distributed zeros on the unit circle, Comput. Meth. Funct. Theory 15 (2015), no. 1, 159–186. [5] E.G. Ganenkova and V.V. Starkov, The Mobius transformation and Smirnov’s inequality for polynomials, Math. Notes 105 (2019), no. 2, 58–68. [6] V.K. Jain, Generalization of certain well-known inequalities for polynomials, Glas. Mat. 32 (1997), 45–51. [7] J.P. Kahane, Some Random Series of Functions, Cambridge University Press, Cambridge, 1985. [8] P.D. Lax, Proof of a conjecture of P. Erd¨os on the derivative of a polynomial, Bull. Amer. Math. Soc. 50 (1944), 509–513. [9] G.G. Lorentz, Approximation of Functions, Chelsea Publishing Company, NewYork, 1986. [10] M.A. Malik and M.C. Vong, Inequalities concerning the derivative of polynomials, Rend. Circ. Mat. Palermo 34 (1985), 422–426. [11] M. Marden, Geometry of polynomials, American Mathematical Society, Providence, 1985. [12] G.V. Milovanovi´c, D.S. Mitrinovi´c and Th. M. Rassias, Topics in Polynomials: Extremal Properties, Inequalities, Zeros, World Scientific Publishing Company, Singapore, 1994. [13] G. Pisier, The Volume of Convex Bodies and Banach Space Geometry, Volume 94, Cambridge University Press, Cambridge, 1989. [14] Q.I. Rahman and G. Schmeisser, Analytic theory of Polynomials, Clarendon Press Oxford, 2002. [15] V.I. Smirnov and N.A. Lebedev, Constructive Theory of Functions of a Complex Variable, Nauka, Moscow, Leningrad, 1964. [16] S. Gulzar, N.A. Rather and F.A. Bhat, The location of critical points of polynomials, Asian-Eur. J. Math. 12 (2019), no. 1, 1950087. | ||
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