Some Properties for Convolution Structures of Holomorphic Functions

In the paper submitted, by employing the linear operator \(I_{\alpha,\beta}^{j}\) defined using the convolution of univalent functions \(k\) and \(h\) belonging to the class \(\mathbb{A}\), which consists of holomorphic functions in the disk \(\mathcal{U =}\left\{ s:s \in \mathbb{C}:|s| < 1 \right\}\) that satisfy the condition \(k(0) = k^{'}(0) - 1 = 0\), we proved that the convolution under this operator belongs to the new class \(\mathfrak{S}_{(\upsilon,\beta,\alpha)(h)}(\Phi)\), according to the concept of the convex hull method of differential subordination, for any convex univalent function mapping the unit disk into the right half-plane, \(\Phi\), in \(\mathcal{U}\) with \(\Phi(0) = 1\).