【摘要】 <正> 1.引言设函数在单位圆|z|<1上是正则的,单叶的.它映照|z|<于|w|<1中.这种f_k（z）的全体形成一函数族 B_k,乃是 k 称的有界单叶函数族.对于 B₁中的函数 f₁（z）,劳宝生讨论了|a|,|z₀|<1,|f₁（z₀）|和|f′（z₀）|四者之间的关系.利用关系式（?）,他的许多结果可以直接推广到函数族B_k中来.但是关于f_k（z）,还有些应该直接研讨的问题.例如当|a|,|z|取定值或|a|,更多还原

【Abstract】 Let the functionbe regular and schlicht in the unit circle |z|<1 and in which let it besuch that |f_k（z）|<1.The totality of all such function forms a class whichshall be denoted by B_k.For a function f₁（z）of B-1 and a point z₀ of |z|<1,R.M.Robinsonhas discussed the relations between the four quantities |α|,|z₀|,|f₁（z₀）|and |f′₁（z₀）|.By means of the relation（?）,some of Robinson’sresults can be extended to the class B_k.However,there are problems in theclass B_k（k>1）which are not allowable to solve them in this manner.Employ the method of parameter representation we obtain the following Theorem.Let f_k（z）∈B_k and write（?）,|α|=|f′_k（0）|,r=|z|<1,then,corresponding to the three cases:1)（?）λ being the least positive root of the equation（?）2)（?）3)（?）we have respectively1)（?）with（?）2)（?）with（?）3)（?）with（?）The estimates 1). 2) and 3) are precise.更多还原