On certain subclasses of univalent p -harmonic mappings

In this paper, the main aim is to introduce the class mathcalU p (lambda,alpha,beta,k 0) of p -harmonic mappings together with its subclasses mathcalU p (lambda,alpha,beta,k 0)capmathcalT p and mathcalU p (lambda,alpha,beta,k 0)capmathcalT 0 p, and investigate the properties of the mappings in these classes. First, we give a sufficient condition for mappings to be in mathcalU p (lambda,alpha,beta,k 0) and also the characterization of mappings in mathcalU p (lambda,alpha,beta,k 0)capmathcalT p for max, fraclambda−frac12lambda+1leqalphaleqlambda. Second, we consider the starlikeness of mappings in mathcalU p (lambda,alpha,beta,k 0)capmathcalT 0 p for max, fraclambda−frac12lambda+1leqalphaleqlambda. Third, extreme points of mathcalU p (lambda,alpha,beta,k 0)capmathcalT p for max0,fraclambda−frac12lambda+1leqalphaleqlambda are found. The support points of mathcalU p (lambda,alpha,beta,k 0)capmathcalT p for max0,fraclambda−frac12lambda+1leqalphaleqlambda and convolution of mappings in mathcalU p (lambda,alpha,beta,k 0)capmathcalT p for max0,fraclambda−frac12lambda+1leqalphaleqlambda are also discussed.