L^q inequalities for polynomials with restricted zeros concerning the growth
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Abstract
If Pn denotes the class of polynomials of degree at most n, then for P ∈ Pn, a consequence of Maximum Modulus theorem yields for R > 1, || P(R, )||∞ < Rn || P ||∞. Various generalizations and refinements of this result are available in literature. In this paper, we consider a general class of polynomials Pn, μ, 1 < μ < n, with restriction on zeros in a specific way and obtain Zygmund-type inequalities concerning the growth of polynomials. Besides obtaining a refinement of a result due to Aziz and Shah, we improve a result of Aziz and Rather.
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Rashid, R., & Shah, W. M. (2024). L^q inequalities for polynomials with restricted zeros concerning the growth. Gulf Journal of Mathematics, 16(1), 193-204. https://doi.org/10.56947/gjom.v16i1.1799
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