Geometric Properties of Some Generalized Mathieu Power Series inside the Unit Disk

We consider two parametric families of special functions: One is defined by a power series generalizing the classical Mathieu series, and other one generalized type involving factorials in its coefficients. Using criteria due to Fejér Ozaki, we provide sufficient conditions for these functions be close-to-convex or starlike inside unit disk, thus univalent. our proofs assisted symbolic computation.