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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.

We know that aMeromorphic function, is an analytic function on domain D such that, its single singular points on domain D, are of pole type. These functions are also called regular functions. Recently, Meromorphic convex functions of order α have been defined and their properties have been investigated. In this paper, at first we introduce the Meromorphic convex functions of inverse order α . In fact, convex functions of order revers α are a special class of analytic functions on unit open disk U that satisfy the following property: R(1+(f^' (z))/(zf^'' (z)))