DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS

被引：0
|
作者：
Jacek DZIOK [1 ]
Ravinder Krishna RAINA [2 ]
Janusz SOKóL [3 ]
机构：
[1] Department of Mathematics, Institute of Mathematics, University of Rzeszów,ul. Rejtana 16A, 35-310 Rzeszów, Poland
[2] M.P. University of Agriculture and Technology
[3] Department of Mathematics, Rzeszów University of Technology,Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
来源：
Acta Mathematica Scientia | 2013年 / 33卷 / 03期
关键词：
Univalent functions; starlike functions; subordination; Fibonacci numbers; tri sectrix of Maclaurin; conchoid of de Sluze;
D O I：
暂无
中图分类号：
O174.13 [凸函数、凸集理论];
学科分类号：
070104 ;
摘要：
This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = { z : | z | < 1 } satisfying the conditions that f （0） = 0, f’（0） = 1, and α(1 + （zf’’（z））/f’（z） + （1-α） （zf’（z））/f（z） ∈P（U）for all z ∈ U , where α is a real number and P（z） = （1 + τ2z2）/（1-τz-τ2z2） （z ∈ U ）.The number τ = （1 -5（1/2））/2 is such that τ2 = 1 + τ . The class SLMα introduced by J. Dziok, R.K. Raina, and J. Sokó [3, Appl. Math. Comput. 218 （2011）, 996 1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.
引用
收藏
页码：609 / 620
页数：12
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