On the derivative of a polynomial with prescribed zeros

• Autorzy: Jain V. K.

Identyfikatory

DOI

10.7862/rf.2017.7

• Języki publikacji: EN

Abstrakty

EN

For a polynomial [wzór] of degree n having all its zeros in │z│ ≤ K, K ≥1 it is known that max [wzór]. By assuming a possible zero of order m, 0 ≤ m ≤ n - 4, at z = 0, of p(z) for n ≥ k + m + 1 with integer k ≥ 3 we have obtained a new refinement of the known result.

Słowa kluczowe

EN

derivative; polynomial; zero of order m at 0; generalization; refinement

PL

pochodna; wielomian; uogólnienie; udoskonalenie

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2017
• Tom: Vol. 40
• Strony: 97--120
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Jain V. K.

• Mathematics Department, I.I.T. Kharagpur, 721302, India

Bibliografia

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• [4] C. Frappier, Q.I. Rahman and St. Ruscheweyh, New inequalities for polynomials, Trans. Amer. Math. Soc. 288 (1985) 69-99.
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• [6] N.K. Govil, On the derivative of a polynomial, Proc. Amer. Math. Soc. 41 (1973) 543-546.
• [7] N.K. Govil, Q.I. Rahman and G. Schmeisser, On the derivative of a polynomial, Ill. J. Math. 23 (1979) 319{329.
• [8] N.K. Govil, Inequalities for the derivative of a polynomial, J. Approx. Theory 63 (1990) 65-71.
• [9] N.K. Govil, Some inequalities for derivatives of polynomials, J. Approx. Theory 66 (1991) 29-35.
• [10] M.A. Malik, On the derivative of a polynomial, J. London Math. Soc. 2 1 (1969) 57-60.
• [11] G. Polya, G. Szegö, Problems and Theorems in Analysis, Vol. 1, Springer-Verlag, Berlin-Heidelberg, 1972.
• [12] P. Turan, Über die Ableitung von Polynomen, Compositio Math. 7 (1940) 89-95.

Uwagi

PL

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