‎A new subclass of Meromorphic univalent functions by using the q-hypergeometric and Hurwitz-Lerch Zeta functions is defined‎. ‎Also‎, ‎by applying the generalized Liu-Srivastava operator on Meromorphic functions‎, ‎some geometric properties of the new defined subclass such as coefficient estimates‎, ‎extreme points‎, ‎convexity and connected set structure are investigated‎.

By considering a fixed point in the punctured unit disk and using the $q$--derivative, a new subfamily of Meromorphic and univalent functions is defined. Also, the first and second order {$q$--derivative} of Meromorphic functions are introduced. Coefficient bounds, extreme points, radii of starlikeness and convexity are obtained. Furthermore, the convexity and preserving under convolution with some restrictions on parameters are investigated

In this study, a broader class of rational functions r(u(z)) of degree mn, where u(z) is a polynomial of degree m is taken into consideration and obtain certain sharp compact generalization of well-known inequalities for rational functions.

Let 𝝨 be the class of Meromorphic bi-univalent functions f of the formf(z)=z+b_0+∑ _(n=1)^∞ ▒ b_n/z^n, which are univalent (analytic and one to one) on the domain Δ ={z∈ C∶ 1.