Inequalities Concerning theLp-Norm of a Polynomial

Some results concerning growth of polynomials

“…(for reference see [11]), the following improvement as well as generalization of a result of Govil and Rahman follows from Theorem 1 by taking β = 0, dividing the two sides by R − 1 and making R → 1.…”

“…24, No.4 (2008) 357 Remark 4. The result of Dewan, Bhat and Pukhta [11] is a special case of Corollay 6, when s = ε = 0.…”

“…By using Theorem 1, we now prove the following result which inter-alia includes a generalization as well as a refinement of a theorem due to Dewan, Bhat and Pukhta [11,Theorem 2].…”

“…By Minkowski's inequality, we get from (35), for every q ≥ 1, Using the inequality (11) and noting that | f (e iθ )| = |e isθ f (e iθ )| = |P(ee iθ )|, 0 ≤ θ < 2π, we get from the inequality (36) 2π 0 P(re iθ ) − P(e iθ ) + mβ ε(R n − q) Proof of Theorem 3. We have by Minkowski's inequality, for every q ≥ 1,…”

“…Dewan,Bhat and Pukhta [11] proved the following generalization as well as a refinement of (5) by involving the coefficients of a polynomial P(z).…”