- 期刊
CONVOLUTIONS OF PRESTARLIKE FUNCTIONS
摘要
The convolution of two functions (The equation is abbreviated) and (The equation is abbreviated) is defined as (f*g) (The equation is abbreviated). For (The equation is abbreviated) and g(z) = z/(1-z)^(2(1-γ)), the extremal function for the class of functions starlike of order γ, we investigate functions h, where h(z)=(f*g)(z), which satisfy the inequality |(zh'/h)-1|/|(zh'/h)+(1-2α)|＜β, 0≤α＜1, 0＜β≤1 for all z in the unit disk. Such functions f are said to be γ-prestarlike of order α and type β. We characterize this family in terms of its coefficients, and then determine extreme points, distortion theorems, and radii of univalence, starlikeness, and convexity. All results are sharp.
延伸閱讀
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