  We call a kind of mappings induced by a kind of weighted Laplace operator as
complex valued kernel $\alpha$-harmonic mappings. In this article, for this
class of mappings, the Heinz type lemma is established, and the best Heinz type
inequality is obtained. Next, the extremal function of Schwartz's Lemma is
discussed. Finally, the coefficients are estimated for the subclass of complex
valued kernel alpha harmonic mappings whose coefficients are real numbers.
