Some Compact Generalization of Bernstein-Type Inequalities Preserved by Modified Smirnov Operator

2025/03/01 by Deepak Kumar, Kumar, Deepak, D. Tripathi +3
Mathematics · #math.CV

paper · pdf · doi:10.48550/arxiv.2503.00328

Abstract

Let P(z) be a polynomial of degree n. In 2004, Aziz and Rather \citeaziz2004some investigated the dependence of |P(Rz)-αP(z)+β\biggl\\biggl((R+1)/(2)\biggr)ⁿ-|α|\biggr\P(z)|, for z ∈ B(\mathbbD), on max_z∈ B(\mathbbD)|P(z)|, for every real and complex number α, β satisfying |α| ≤ 1, |β| ≤ 1, and R ≥ 1. This paper presents a compact generalization of several well-known polynomial inequalities using modified Smirnov operator, demonstrating that the operator preserves inequalities between polynomials.

Related

• Generalization of Some Well-Known Polynomial Inequalities for the Modified Smirnov Operator
• Bernstein-type Inequalities Preserved by Modified Smirnov Operator
• Certain Bernstein-type L_p inequalities for polynomials
• On operators preserving inequalities between polynomials
• Bernstein- and Markov-type inequalities