On the derivative of a polynomial

• Autorzy: Jain Vinay Kumar

Identyfikatory

DOI

10.7862/rf.2023.1

• Języki publikacji: EN

Abstrakty

EN

For an arbitrary polynomial P(z), let M(P,r) =max|z|=r|P(z)| and m(P,r)=min|z|=r|P(z)|, (r >0). For a polynomial p(z)=Pn [wzór] of degreen, having all its zeros in|z|≤k, (k≥1), with a zero of orders, (s≥0), at 0 and F0, F1, F2, Gn-s, F3, F4, Hn-s, Fn-s, B0, B1, En-1, B2, B3, Dn-1 and Bn-1, as in Theorem, we have obtained a refinement [wzór] of our old result (1997), there by obtaining a new refinement of known results [wzór].

Słowa kluczowe

EN

polynomial; derivative; lower bound for M (p′1); zero of order s at 0; refinement

PL

wielomian; pochodna; udoskonalenie

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2023
• Tom: Vol. 46
• Strony: 5--13
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Jain Vinay Kumar

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

• https://orcid.org/0000-0003-2382-2499

Bibliografia

• [1] A. Aziz, Inequalities for the derivative of a polynomial, Proc. Am. Math. Soc. 89 (1983) 259-266.
• [2] A. Aziz, Q.M. Dawood, Inequalities for a polynomial and its derivative, J. Approx. Theory 54 (1988) 306-313.
• [3] C. Frappier, Q.I. Rahman, St. Ruscheweyh, New inequalities for polynomials, Trans. Am. Math. Soc. 288 (1985) 69-99.
• [4] N.K. Govil, On the derivative of a polynomial, Proc. Am. Math. Soc. 41 (1973) 543-546.
• [5] N.K. Govil, Inequalities for the derivative of a polynomial, J. Approx. Theory 63 (1990) 65-71.
• [6] V.K. Jain, On the derivative of a polynomial, Approximation Theory Appl. 13 (1997) 88-96.
• [7] V.K. Jain, On the derivative of a polynomial with prescribed zeros, J. Math. Appl. 40 (2017) 97-120.
• [8] M.A. Malik, On the derivative of a polynomial, J. Lond. Math. Soc. (2) 1 (1969) 57-60.
• [9] P. Turán, Über die albeitung von polynomen, Compos. Math. 7 (1939) 89-95.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).