‎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.

Following a recent work of Chademan-Mirzapour (1995&1999). we generalize the classical theorems of Jensen, Bernstein-Doetsch, Ostrowski, Blumberg-Sierpinski and Mehdi on approximately midconvex functions in real vactor spaces to approximately midconvex functions on topological groups. We define also E -Wright-convexity in topological groups and prove a theorem on it

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.

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