Let \(A_{p}(n)\) denote the class of functions \(f\) of the following form: \[ \displaystyle{f(z)=z^{p}+\sum^{\infty}_{k=n}a_{p+k}z^{p+k}}\, \, (p,n\in\mathbf{N}:=\{ 1,2,3,\dots \} )\, , \] which are analytic and \(p\)-valent in the open unit disk. The authors introduced some interesting subclasses of \(A_{p}(n)\) as follows. Definition 1. A function \(f\in A_{p}(n)\) is said to be in the class \(R_{p,j}(n,A,B)\) if it satisfies the following subordination condition: \[ \displaystyle{ \frac{(p-j)!}{p!}\frac{f^{(j)}(z)}{z^{p-j}}\prec \frac{1+Az}{1+Bz}}\, \, (z\in U\, ;\, 0\leq j\leq p)\, , \] where \(A\) and \(B\) are arbitrarily fixed real numbers constrained by \(-1\leq B