- 期刊
CONVOLUTION AND DIFFERENTIAL SUBORDINATION
摘要
Let A denote the class of all functions f analytic in the open unit disc U with f(0) = 0 = f'(0)-1. Let h be any convex univalent analytic function on U with h(0) = 1 and Re h(z) ＞ 0 in U. Let g A be fixed. Denote by S_g (h) the class of all g functions f ε A such that, g*f(z) ≠ 0 in U and a(g*f)'(Z)/(g*f)(z) ＜ h(z), z ε U (＜ denote subordination). It is proved in this paper that the class S_g(h) is closed under convolution with convex functions. It has also been established that S_g(h) ⊆ S_(Φ*g)(h) where Φ is any convex univalent function in A. Four other classes are also defined and studied using mainly the convex hull method and the methd of differential subordination.
延伸閱讀
- Li, Y. A. (1996). A Study of Subordinating Adverbial Conjunction. 復興崗學報, (58), 39-51. https://www.airitilibrary.com/Article/Detail?DocID=04298063-199609-201011110008-201011110008-39-51
- OSIKIEWICZ, J. A., & KHAN, M. K. (2004). INCLUSION RESULTS FOR CONVOLUTION SUBMETHODS. International Journal of Mathematics and Mathematical Sciences, 2004(), 55-64-005. https://doi.org/10.1155/S0161171204301511
- Marikkannan, N., & Ganesamoorthy, C. (2008). On Applications of Differential Subordination and Superordination. Tamkang Journal of Mathematics, 39(2), 155-164. https://www.airitilibrary.com/Article/Detail?DocID=00492930-200806-39-2-155-164-a
- Mahzoon, H. (2011). On Certain Subclasses of Analytic Functions Defined by Differential Subordination. International Journal of Mathematics and Mathematical Sciences, 2011(), 10-19-001. https://doi.org/10.1155/2011/103521
- YAKUBOVICH, S., & KALLA, S. L. (1993). ON A NEW APPROACH TO CONVOLUTION CONSTRUCTIONS. International Journal of Mathematics and Mathematical Sciences, 1993(), 435-448. https://doi.org/10.1155/S0161171293000559