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On a Composition Preserving Inequalities between Polynomials

  • Functional Analysis
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Abstract

The Schur-Szegö composition of two polynomials \(f\left( z \right) = \sum\nolimits_{j = 0}^n {{A_j}{z^j}} \) and \(g\left( z \right) = \sum\nolimits_{j = 0}^n {{B_j}{z^j}} \), both of degree n, is defined by \(f * g\left( z \right) = \sum\nolimits_{j = 0}^n {{A_j}{B_j}{{\left( {\begin{array}{*{20}{c}} n \\ j \end{array}} \right)}^{ - 1}}{z^j}} \). In this paper, we estimate the minimum and the maximum of the modulus of f * g(z) on z = 1 and thereby obtain results analogues to Bernstein type inequalities for polynomials.

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Authors and Affiliations

  1. S.P.College, Srinagar, India

    S. Gulzar

  2. Kashmir University, Srinagar, India

    N. A. Rather

Authors
  1. S. Gulzar
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  2. N. A. Rather
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Correspondence to S. Gulzar.

Additional information

Original Russian Text © S. Gulzar, N.A. Rather, 2018, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2018, No. 1, pp. 45-52.

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Gulzar, S., Rather, N.A. On a Composition Preserving Inequalities between Polynomials. J. Contemp. Mathemat. Anal. 53, 21–26 (2018). https://doi.org/10.3103/S1068362318010041

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  • DOI: https://doi.org/10.3103/S1068362318010041

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