Two Different Improved Bounds of Rivlin's Type Inequality on Polynomial Diversified under the Same Hypotheses

Abstract

Let p(z) be a complex polynomial of degree n. The problem of best approximation under different restrictions on the zeros had been attracting many, including renowned scientists and mathematicians like Mandeleev, Markov brothers and Bernstein. Their works had been studied extensively by many mathematicians which resulted in rich collection of inequalities concerning complex polynomials. In this article, we discuss in brief two different improved bounds of Rivlin's type inequality on polynomial diversified under the same hypotheses.