We construct polynomial norming meshes with optimal cardinality growth, on planar compact starlike domains that satisfy a Uniform Interior Ball Condition (UIBC). 2000 AMS subject classification: 41A10, 41A63, 65D05.

By using the method of differential subordinations, we derive certain sufficient conditions for strongly starlike functions associated with an integral operator. All these results presented here are sharp. 2000 Mathematics Subject Classification. Primary 30C45; Secondary 30A10.

In this paper we will study the integral operator involving Bessel functions of the first kind and of order v.We will investigate the integral operator for the classes of starlike and convex functions in the open unit disk.

In this paper, we define a new subclass Ao(A, B) of univalent functions and investigate several interesting characterization theorems involving a general class S" [A, B] of starlike functions

By using functions of bounded variation we generalize the class of strongly starlike functions and related classes. The main object is to obtain characterizations and inclusion properties of these classes of functions.

The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequen...