On the maximum modulus of a complex polynomial

Authors : Shabir MALİK, Ashish KUMAR

Pages : 666-681

Doi:10.31801/cfsuasmas.989344

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Publication Date : 2022-09-30

Article Type : Research Paper

Abstract :In this paper we impose distinct restrictions on the moduli of the zeros of p insert ignore into journalissuearticles values( z ); = n ∑ v = 0 a v z v pinsert ignore into journalissuearticles values(z);=∑v=0navzv and investigate the dependence of ∥ p insert ignore into journalissuearticles values( R z ); − p insert ignore into journalissuearticles values( σ z ); ∥ ‖pinsert ignore into journalissuearticles values(Rz);−pinsert ignore into journalissuearticles values(σz);‖ , R > σ ≥ 1 R>σ≥1 on M α Mα and M α + π Mα+π , where M α = max 1 ≤ k ≤ n | p insert ignore into journalissuearticles values( e i insert ignore into journalissuearticles values( α + 2 k π ); / n ); | Mα=max1≤k≤n|pinsert ignore into journalissuearticles values(eiinsert ignore into journalissuearticles values(α+2kπ);/n);| and on certain coefficients of p insert ignore into journalissuearticles values( z ); pinsert ignore into journalissuearticles values(z); . This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases. Moreover, the problem of estimating p insert ignore into journalissuearticles values( 1 − w n ); pinsert ignore into journalissuearticles values(1−wn); , $0 Keywords : Polynomials, definite integral, zeros, inequalities

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