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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