Author/Authors :
qiao, j. , chen, j. , shi, m.
Abstract :
In this paper, the main aim is to introduce the class mathcalUp(lambda,alpha,beta,k0) of p-harmonic mappings together
with its subclasses mathcalUp(lambda,alpha,beta,k0)capmathcalTp and mathcalUp(lambda,alpha,beta,k0)capmathcalT0p, and
investigate the properties of the mappings in these classes. First,
we give a sufficient condition for mappings to be in mathcalUp(lambda,alpha,beta,k0) and also the characterization of
mappings in mathcalUp(lambda,alpha,beta,k0)capmathcalTp for max0,fraclambda−frac12lambda+1leqalphaleqlambda. Second, we consider the starlikeness of
mappings in mathcalUp(lambda,alpha,beta,k0)capmathcalT0p for max0,fraclambda−frac12lambda+1leqalphaleqlambda. Third, extreme points of mathcalUp(lambda,alpha,beta,k0)capmathcalTp for
max0,fraclambda−frac12lambda+1leqalphaleqlambda are found. The support points of mathcalUp(lambda,alpha,beta,k0)capmathcalTp for
max0,fraclambda−frac12lambda+1leqalphaleqlambda and convolution of mappings in mathcalUp(lambda,alpha,beta,k0)capmathcalTp for
max0,fraclambda−frac12lambda+1leqalphaleqlambda are also discussed.
Keywords :
p-harmonic mapping , uniform convexity , uniform starlikeness , extreme point , support point
