On inequality |zⁿ-1|≥|z-1|

2014/06/04 by Radoš Bakić, Rados Bakic, Bakic, Rados
Mathematics · #Analytic Number Theory Research #Mathematics and Applications #Point processes and geometric inequalities #math.CV

paper · pdf · doi:10.48550/arxiv.1406.1166

arxiv created 2014/06/04 · arxiv updated 2014/06/06

Abstract

It is known that inequality |zⁿ-1|≥|z-1| holds on the circle |z-1/2|= 1/2, where n is a positive integer. We prove that in fact n can be real number not less then 1. We also prove following inequality as a lemma: cosⁿx\lt 1-sinx for real n\gt3 and 2π/(n+1)≤ x \lt π/2.

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