scholarly journals Hierarchical Composition of Self-Stabilizing Protocols Preserving the Fault-Containment Property

2009 ◽  
Vol E92-D (3) ◽  
pp. 451-459 ◽  
Author(s):  
Yukiko YAMAUCHI ◽  
Sayaka KAMEI ◽  
Fukuhito OOSHITA ◽  
Yoshiaki KATAYAMA ◽  
Hirotsugu KAKUGAWA ◽  
...  
Keyword(s):  
Containment Property

scholarly journals A CONVOLUTION APPROACH TO CERTAIN SUBCLASSES OF STARLIKE FUNCTIONS

1992 ◽  
Vol 23 (4) ◽  
pp. 311-320
Author(s):  
T . RAM REDDY ◽  
O. P. JUNEJA ◽  
K. SATHYANARAYANA
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Integral Transforms ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disc ◽  
Containment Property ◽  
Convolution Approach

The class $R_\gamma(A,B)$ for $-1\le B < A\le 1$ and $\gamma> (A- 1)/(1- B)$ consisting of normalised analytic functions in the open unit disc is defined with the help of Convolution technique. It consists of univalent starlike functions for $\gamma\ge 0$. We establish containment property, integral transforms and a sufficient condition for an analytic function to be in $R\gamma(A,B)$. Using the concept of dual spaces we find a convolution condition for a function in this class.

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