Integral norm estimates for the polar derivative of Lacunary-type complex polynomials

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extensions of some polynomial inequalities to the polar derivative

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15 صفحه اول

Application of the Norm Estimates for Univalence of Analytic Functions

By using norm estimates of the pre-Schwarzian derivatives for certain family of analytic functions, we shall give simple sufficient conditions for univalence of analytic functions.

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On the polar derivative of a polynomial

For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...

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A Comparative Analysis of Bernstein Type Estimates for the Derivative of Multivariate Polynomials

We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in points of some domain, where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses into the convex domain K. The other, pluripotential theoretic approach, mainly due to Baran, works for even more gene...

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Divisibility Test for Lacunary Polynomials

Given two lacunary (i.e. sparsely-represented) polynomials with integer coefficients, we consider the decision problem of determining whether one polynomial divides the other. In the manner of Plaisted [6], we call this problem 2SparsePolyDivis. More than twenty years ago, Plaisted identified as an open problem the question of whether 2SparsePolyDivis is in P [7]. Some progress has been made si...

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ژورنال

عنوان ژورنال: Applicable Analysis and Discrete Mathematics

سال: 2020

ISSN: 1452-8630,2406-100X

DOI: 10.2298/aadm200412036m