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Convexity and starlikeness of functions defined by a class of integral operators

 

作者: Rosihan M. Ali,   Vikramaditya Singh,  

 

期刊: Complex Variables, Theory and Application: An International Journal  (Taylor Available online 1995)
卷期: Volume 26, issue 4  

页码: 299-309

 

ISSN:0278-1077

 

年代: 1995

 

DOI:10.1080/17476939508814791

 

出版商: Gordon and Breach Science Publishers

 

关键词: 30C45;30C45

 

数据来源: Taylor

 

摘要:

For A : [0,1] → R real-valued monotone decreasing function on [0,1] satisfying A(l)=0tA(t)→ 0 ast→0+ andtA′(t)/(l−t2) increasing on (0,1), we show thatMA(f) ≥ 0forfclose-to-convex whereThis is analogous to a recent result of Fournier and Ruscheweyh [2]. Analogously we obtain least value ofβso that forganalytic in, the functionsandare convex. Here2F1is the Gaussian hypergeometric function. These results are extended to convexity and order of convexity of convex combinations of the formρz +(1−ρ)F(z)ρ< 1. Corresponding starlikeness results in [2] are also extended to such convex combinations.

 

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