Geodesic
On Erdös-lax inequality concerning polynomials
Filomat, Tome 36 (2022) no. 18, p. 6123

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DOI

Recently Milovanović et al. [Bulletin T.CLIII de l'Académie Serbe des sciences et des arts - 2020.] proved that if P(z) ∈ Pn with no zeros in |z| k, k ≥ 1, then,∣∣∣P′(z)∣∣∣ ≤ ∥P∥ 2 [ n − { n ( k − 1 k + 1 ) + 2 k + 1 ( |c0| − kn|cn| |c0| + kn|cn| )} |P(z)|2 ∥P∥2 ] , |z| = 1, where P(z) = c0 + c1z + · · · + cnzn ∈ Pn is a polynomial of degree n. In this paper, we obtain some results concerning the class of polynomials having s−fold zero at origin. These results not only generalizes but also refines many well-known results due to Milovanović.
DOI : 10.2298/FIL2218123W
Classification : 30A10, 30C10, 30C15
Keywords: Bernstein-type inequalities, Extremal coefficients, Erdös-Lax inequality 
Irfan Ahmad Wani; Ishfaq Nazir; Mohammad Ibrahim Mir. On Erdös-lax inequality concerning polynomials. Filomat, Tome 36 (2022) no. 18, p. 6123 . doi: 10.2298/FIL2218123W
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     title = {On {Erd\"os-lax} inequality concerning polynomials},
     journal = {Filomat},
     pages = {6123 },
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     doi = {10.2298/FIL2218123W},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2218123W/}
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