Let \({\mathcal A}\) be the class of functions \(f(z)=z+\sum_{k=2}^\infty a_kz^k\) that are analytic in the unit disc \({\mathcal U}=\{z:|z|<1\}.\) For any integer \(n,\) \(\lambda\geq 0\) and \(f\in {\mathcal A}\) a multiplier transformation is defined by \[ I_n^\lambda f(z)=z+\sum_{k=2}^\infty k\left(\frac{1+\lambda}{k+\lambda}\right)^n a_kz^k. \] Further, for \(0\leq\gamma<1\) and \(0<\delta\leq 1,\) the class \({\mathcal K}_n^\lambda(\gamma,\delta,\eta,A,B)\) consists of functions \(f\in {\mathcal A}\) satisfying \[ \left|\arg\left(\frac{z\left(I_n^\lambda f(z)\right)'}{I_n^\lambda g(z)}-\gamma\right)\right|<\delta\frac{\delta}{2},\quad z\in{\mathcal U}, \] for some \(g\in {\mathcal S}_n^\lambda (\eta,A,B),\) where \[ {\mathcal S}_n^\lambda (\eta,A,B)=\left\{g\in{\mathcal A}: \frac{1}{1-\eta}\left(\frac{z\left(I_n^\lambda g(z)\right)'}{I_n^\lambda g(z)}-\eta\right)\prec \frac{1+Az}{1+Bz}\right\} \] and ``\(\prec\)'' denotes the usual subordination. In this paper, the authors give the basic inclusion relationships among the classes \({\mathcal K}_n^\lambda(\gamma,\delta,\eta,A,B)\) and some integral preserving properties in connection with the operator \(I_n^\lambda.\)