Some Properties for Convolution Structures of Holomorphic Functions

In the paper submitted, by employing the linear operator \(Iα,βʲ\) defined using the convolution of univalent functions \(k\) and \(h\) belonging to the class \(A\), which consists of holomorphic functions in the disk \(U =\{ s:s ∈ C:|s| < 1 \}\) that satisfy the condition \(k(0) = k'(0) - 1 = 0\), we proved that the convolution under this operator belongs to the new class \(S(υ,β,α)(h)(Φ)\), 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, \(Φ\), in \(U\) with \(Φ(0) = 1\).