Extremal Problems of Bernstein-Type and an Operator Preserving Inequalities between Polynomials
Gradimir V. Milovanović, Abdullah Mir, Adil Hussain
Abstract
Under consideration are the well-known extremal problems of Bernstein-type which relate the uniform norm between polynomials on the unit disk in the plane. We establish a few new inequalities in both directions for the generalized $ {\mathcal{B}}_{n} $ -operator while accounting for the placement of the zeros of the underlying polynomials. Also, we obtain various estimates for the maximum modulus of a polynomial as well as some inequalities of Erdös–Lax type.
Topics & Concepts
MathematicsBernstein polynomialType (biology)Operator (biology)Unit diskNorm (philosophy)PolynomialPure mathematicsComplex planeDifference polynomialsBernstein inequalitiesInequalityMathematical analysisOrthogonal polynomialsGenePolitical scienceBiologyEcologyBiochemistryRepressorChemistryTranscription factorLawMathematical functions and polynomialsMathematical Approximation and IntegrationAnalytic and geometric function theory