Estimates for the polar derivative of a constrained polynomial on a disk

• Autores: Gradimir V. Milovanovic, Abdullah Mir, Adil Hussain
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 24, Nº. 3, 2022, págs. 541-554
• Idioma: inglés
• DOI: 10.56754/0719-0646.2403.0541
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Este trabajo es parte de una reciente ola de estudios sobre desigualdades que relacionan la norma uniforme de un polinomio univariado con coeficientes complejos con su derivada en el disco unitario en el plano. Cuando existe un límite sobre los ceros de un polinomio, desarrollamos algunas desigualdades adicionales que relacionan la norma uniforme del polinomio con su derivada polar. Los resultados obtenidos satisfacen desigualdades de tipo Erdὄs-Lax y Turán para polinomios restringidos recientemente establecidas, y también producen desigualdades que son más estrictas que aquellas conocidas previamente en la larga literatura dedicada a este tema.

  • English

    Abstract This work is a part of a recent wave of studies on inequalities which relate the uniform-norm of a univariate complex coefficient polynomial to its derivative on the unit disk in the plane. When there is a limit on the zeros of a polynomial, we develop some additional inequalities that relate the uniform-norm of the polynomial to its polar derivative. The obtained results support some recently established Erdὄs-Lax and Turán-type inequalities for constrained polynomials, as well as produce a number of inequalities that are sharper than those previously known in a very large literature on this subject.

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