Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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INEQUALITIES FOR B-OPERATOR

  • Akhter, Rubia (Department of Mathematics, University of Kashmir) ;
  • Gulzar, M.H. (Department of Mathematics, University of Kashmir)
  • Received : 2022.05.29
  • Accepted : 2022.09.14
  • Published : 2022.09.30
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Abstract

Let 𝓟n denote the space of all complex polynomials $P(z)=\sum\limits_{j=0}^{n}{\alpha}_jz^j$ of degree n. Let P ∈ 𝓟n, for any complex number α, DαP(z) = nP(z) + (α - z)P'(z), denote the polar derivative of the polynomial P(z) with respect to α and Bn denote a family of operators that maps 𝓟n into itself. In this paper, we combine the operators B and Dα and establish certain operator preserving inequalities concerning polynomials, from which a variety of interesting results can be obtained as special cases.

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References

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