Some subclasses of close-to-convex mappings associated with conic regions
In this paper, we introduce and investigate several new subclasses of close-to-convex functions and their related mappings. Various interesting properties including sufficiency criteria, coefficient estimates, arc-length problem and radius of convexity are investigated.
Coefficient inequalities for Janowski-Sakaguchi type functions associated with conic regions
The purpose of the present paper is to introduce and study some new subclasses of Sakaguchi-type functions defined by using the concept of Janowski functions in conic regions. Various interesting properties such as sufficiency criteria, coefficient estimates and distortion result are investigated for these function classes.
On a certain univalent mapping.
Then $f(z)$ is said to be starlike with respect to symmetrical points. Obviously the class of functions univalent and starlike with respect to symmetrical points includes the classes of convex functions and odd functions starlike with respect to the origin. THEOREM 1. Let $ f(z)=z+\cdots$ be regular in $|z|<1$ . Then a necessary and sufficient condition for $f(z)$ to be univalent and starlike with respect to symmetrical points in $|z!<1$ is that