摘要
对于首一多项式Ｐ（ｚ）＝ｚｎ＋ａ１ｚｎ－１＋…＋ａｎ，ｎ≥２，Ｆ是其Ｊｕｌｉａ集，Ｐ．Ｂｈａｔｔａｃｈａｒｙｙａ和Ｙ．Ｅ．Ａｒｕｍａｒａｊ［１］猜测ｄ（Ｆ）≥２，这里ｄ（Ｆ）表示Ｆ的直径．本文中，我们将证明对于复平面上任何紧Ｅ有不等式ｄ（Ｅ）≥２·ｃａｐ（Ｅ）成立，这里ｃａｐ（Ｅ）表示Ｅ的对数容量［１］，作为推论，我们证明了上述猜测．
For any monic polynomial p(z)= z￣n + a_1z￣(ng1) + … + a_n,n≥2,F is the Julia set, P.Bhattacharyya and Y. E. Arumaraj[1] conjectured d (F) ≥2,where d (F) is the diameter ofF. In this note. We will prove d(E)≥2. cap(E)for any compact set E on a,cap(E) isthe logarithemic capacity of E. As a corollary, we prove the above conjecture.
