In this paper we discuss about convex combinations of the form \(\mathcal {K}_{n,\lambda }^{\alpha ,\beta }=(1-\lambda )\Psi _{n,\alpha }+\lambda \Psi _{n,\beta }\) of Graham-Kohr type extension operators \(\Psi _{n,\alpha }\) , where \(\lambda \in [0,1]\) and \(\alpha ,\beta \in [0,1]\) . The operators \(\Psi _{n,\alpha }\) were defined by I. Graham and G. Kohr in Complex Variables Theory Appl. 47 (2002), 59-72. They proved that the extension operator \(\Psi _{n,\alpha }\) preserve the starlikeness for all \(n\ge {2}\) and \(\alpha \in [0,1]\) . The main idea of this paper is to obtain new extension operators defined by convex combinations of Graham-Kohr type operators \(\Psi _{n,\alpha }\) that preserve the starlikeness. We prove that a starlike function \(f\in S^*\) with \(\mathfrak {Re}f'(z_1)>0\) , for all \(z_1\in \mathbb {U}\) , is taken to a starlike mapping on the Euclidean unit ball \(\mathbb {B}^n\) by the operators \(\mathcal {K}_{\lambda }^{0}\) and \(\mathcal {K}_{\lambda }^{1}\) , where \(\mathcal {K}_{\lambda }^{0}\) and \(\mathcal {K}_{\lambda }^{1}\) are particular forms of the operator \(\mathcal {K}_{n,\lambda }^{\alpha ,\beta }.\)
