Relations among starlikeness, convexity and k-fold symmetry of locally biholomorphic mappings in Cn

The starlikeness, convexity, covering theorem and extreme points of p-harmonic mappings

The main aim of this paper is to introduce three classes $H^0_{p,q}$, $H^1_{p,q}$ and $TH^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. First, we discuss the starlikeness and convexity of mappings in $H^0_{p,q}$ and $H^1_{p,q}$. Then establish the covering theorem for mappings in $H^1_{p,q}$. Finally, we determine the extreme points of the class $TH^*_{p}$.

Close-to-convexity, starlikeness, and convexity of certain analytic functions

‘The present investigation was supported, in part, by the Japanese Ministry of Education, Science and Culture tinder Grant-in-Aid for General Scientific Research (No. 046204) and, in part, by the Natural Sciences and Engineering Research Council of Canada under Grant 0GP0007353. A preliminary report on this paper was presented at the spring meeting of the Mathematical Society of Japan held at W...

the starlikeness, convexity, covering theorem and extreme points of p-harmonic mappings

the main aim of this paper is to introduce three classes $h^0_{p,q}$, $h^1_{p,q}$ and $th^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. first, we discuss the starlikeness and convexity of mappings in $h^0_{p,q}$ and $h^1_{p,q}$. then establish the covering theorem for mappings in $h^1_{p,q}$. finally, we determine the extreme points of the class $th^*_{p}$.

Approximate Convexity and Submonotonicity in Locally Convex Spaces

Subordination Criteria for Starlikeness and Convexity

For functions p analytic in the open unit disc U = {z : |z|< 1} with the normalization p(0)= 1, we consider the families [A,−1], −1 0, consisting of p, which have the disc formulation |p−1|< b in U . We then introduce subordination criteria for the choice of p(z)= zf ′(z)/f(z), where f is analytic in U and n...