| 关于某些单叶调和函数 |
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| 引用本文： | 周亚晶,刘礼泉,陈莉莉.关于某些单叶调和函数[J].黑龙江大学自然科学学报,2007,24(5):696-700. |
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| 作者姓名： | 周亚晶 刘礼泉 陈莉莉 |
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| 作者单位： | 黑龙江大学,数学科学学院,哈尔滨,150080 |
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| 摘 要： | 用H表示形如f(z)=h(z) (g(z))的调和函数族,其中h和g是单位圆盘内的解析函数.考虑日的三类子族函数.其中的两族为PH(α)={f:Re(f(z)/z)≥α}和NH(α)={f:Re((e)f(z)/(e)θ/(e)z/(e)θ)≥α},),式中0≤α＜1和θ=argz.得到了函数f属于其中一族的一个充分必要条件,并且获得了一些系数不等式和模的估计.当h(z)-z具有负系数g(z)具有正系数时,得到这几类函数族之间的包含关系、偏差性质和极值点等.
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| 关 键 词： | 调和 解析 星象 凸象 harmonic analytic starlike convex 单叶调和函数 harmonic functions positive negative coefficients distortion theorems extreme points inclusion relations inequalities estimates module necessary condition classes analytic unit disk 极值点 偏差性质 包含关系 |
| 文章编号： | 1001-7011(2007)05-0696-05 |
| 修稿时间： | 2006年7月14日 |
On certain classes of univalent harmonic functions |
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| Zhou Yajing,Liu Liquan,Chen Lili.On certain classes of univalent harmonic functions[J].Journal of Natural Science of Heilongjiang University,2007,24(5):696-700. |
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| Authors: | Zhou Yajing Liu Liquan Chen Lili |
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| Abstract: | A function f(z)=h(z)+(g(z))is called harmonic in the unit disk △={z:|z|＜1},if h(z) and g(z) are analytic in △.The authors consider three subclasses of the class of univalent harmonic functions in the unit disk.Two of them are PH(α)={f:Re(f(z)/z)≥α}and NH(α)={f:Re((e)f(z)/(e)θ/(e)z/(e)θ)≥α},where O≤a＜1 and θ=argz.A sumcient and necessary condition that the function f belongs to one of these classes is shown.The authors obtain some coefficient inequalities and the estimates of module.Some inclusion relations, distortion theorems and extreme points for these classes are obtained if h(z)-z has negative coefficients and g(z) has positive coefficients. |
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| Keywords: | harmonic analytic starlike convex |
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