In this paper, we study the class \(\mathcal {A}(p)\) which includes functions f that are meromorphic in the unit disk \(\Delta \) and have a simple pole at \(z=p\) for some \(p\in (0,1)\) with the normalization \(f(0)=0=f'(0)-1\) . We establish a sufficient condition for functions in this class to be univalent. Making use of this condition, we introduce a subfamily of \(\mathcal {A}(p)\) consisting of univalent functions satisfying a certain differential inequality in \(\Delta \) . Next, we obtain a representation formula for such functions. Additionally, we establish necessary and sufficient conditions on the coefficients \(b_n\) for functions \(f\in \mathcal {A}(p)\) of the form \(\begin{aligned} \frac{z}{f(z)}=1+b_1 z+b_2z^2+\cdots , \quad z\in \Delta , \end{aligned}\) to belong to this class. Furthermore, we determine sharp upper bounds for \(|b_n|\) for all \(n\ge 2\) . Finally, we establish a sharp estimate for the Fekete-Szegö functional associated with the newly introduced subclass.
