inthis paper, the main aim is to introduce the class $mathcal{u}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p$ and $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p^0$, andinvestigate the properties of the mappings in these classes. first,we give a sufficient condition for mappings to be in $mathcal{u}_p(l...